Unless otherwise stated, the Stochastics Seminar takes place on Wednesday, 15:3016.15, in room 610 or 611 of the Math building.
Up next
Future talks
Recent past
May 11, 2017
Room 610
1:30  2:15
 Wioletta Ruszel (TU Delft)

Longrange Ising models: phase transitions and interfaces

May 3, 2017 Room 611
 Sandjai Bhulai (VU Amsterdam)

Value Function Discovery In Markov Decision Processes

April 26, 2017
Room DDW 1.22
 Sandór Kolumbán (TU/e)

Criticality in the brain, what we can and cannot see

April 19, 2017
 Matej Stehlik (Université Grenoble Alpes)

Edge and facewidth of projective quadrangulations

March 29, 2017 Room 611
 Karma Dajani (Utrecht)

Invariant measures, matching and the frequency of 0 for signed binary expansions

March 1, 2017 Room 611
 Derong Kong (Leiden)

On the bifurcation set of unique Expansions

February 22, 2017 Room 610
 Reka Szabo (Groningen)

From survival to extinction of the contact process by the removal of a single edge

February 15, 2017 Room 611
 Reem Yassawi (Trent University, Canada)

Random orders on Bratteli diagrams

January 26  27, 2017

STAR workshop on Random Graphs 2017 (Utrecht)


December 21, 2016

Francesca Collet (Delft)

Selfsustained oscillations in dissipative mean field interacting particle systems

December 14, 2016
Room 611

Christian Spitoni (postponed) (Utrecht)

t.b.a.

December 7, 2016

Luca Avena (Leiden)

RW kernels, spanning forests and multiscale analysis on graphs.

November 30, 2016

Arnoud den Boer (UvA)

Decisionbased model selection

November 23, 2016

Maria Remerova (UvA)

Queueing systems with random fluid limits

October 26, 2016

Mathew Penrose (Bath, UK)

The strong giant in a random digraph

October 18, 2016
11:15  12:00

Moumanti Podder (NYU)

The strange logic of GaltonWatson trees

September 28, 2016

Johan van Leeuwaarden (TU/e)

Solvable random network model for disordered sphere packings in all dimensions

September 5, 2016
13:00  13:45

Alessandra Cipriani (WIAS Berlin)

The Membrane model

June 28, 2016

David Coupier (Lille 1)

Navigation on Geometric Random Graphs

June 21, 2016

Willem van Zuijlen (Leiden)

Meanfield GibbsnonGibbs transitions

June 16, 2016
10:00  10:45

Matej Stehlik (Université Grenoble Alpes)

Topological bounds on the chromatic number

June 7, 2016

Rene Conijn (Utrecht)

Largest clusters in Percolation and Conformal Measure Ensembles

31 May 2016

Federico Camia (NYU Abu Dhabi)

From Brownian Loops to Conformal Fields

24 May 2016

Christoph HoferTemmel (NLDA Den Helder)

Disagreement percolation for the hardsphere model

Wednesday 18 May 2016
15:00, Room 610

Krerley Oliveira (Universidade Federal de Alagoas, Maceió Brazil)

On Uniqueness of Equilibrium States for some Iterated Function Systems

10 May 2016
11:15, Room 610

Shota Gugushvili (Leiden)

Posterior contraction rate for nonparametric Bayesian estimation of the dispersion coefficient of a stochastic differential equation

More distant past
Lists of stochastics talks that took place in the seminar before 2016
can be found here, here,
here, here
and here.
Abstracts
Speaker:

Shota Gugushvili (Leiden)

Title:

Posterior contraction rate for nonparametric Bayesian estimation of the dispersion coefficient of a stochastic differential equation

Abstract:

We consider the problem of nonparametric estimation of the deterministic dispersion coefficient of a stochastic differential equation based on discrete time observations on its solution. We take a Bayesian approach to the problem and under suitable regularity assumptions derive the posterior contraction rate. This rate turns out to be the optimal posterior contraction rate.
Joint work with Peter Spreij.

Speaker:

Krerley Oliveira (Universidade Federal de Alagoas, Maceió Brazil)

Title:

On Uniqueness of Equilibrium States for some Iterated Function Systems

Abstract:

In this talk we discuss two recent results on uniqueness of equilibrium states for some IFS.
In the first setting, we prove existence of relative maximal entropy measures for certain random dynamical systems
that are skew products of the type $F(x,y)=(\theta(x), f_x(y))$, where $\theta$ is an invertible map preserving an
ergodic measure $\mathbb{P}$ on a Polish space and $f_x$ is a local diffeomorphism of a compact Riemannian manifold
exhibiting some nonuniform expansion. As a consequence of our proofs, we obtain an integral formula for the
relative topological entropy as the integral the of logarithm of the topological degree of $f_x$ with respect to
$\mathbb{P}$. When $F$ is topologically exact and the supremum of the topological degree of $f_x$ is finite, the
maximizing measure is unique and positive on open sets.
The second setting we discuss uniqueness of equilibrium states for Partially Hyperbolic Horseshoes studied in a
previous article with R. Leplaideur and I. Rios and in a previous article by Diaz, Horita, Sambarino and Rios. These
families of horseshoes have interesting features, as dense sets of segments in its central direction on its non
wandering set. They have heteroclinical cycles and are extensions of the golden shift. From one hand, they have
phase transitions for smooth potentials. From the other hand, one expect uniqueness for potentials that are close to
zero. We make use of the semiconjugacy with the shift to caracterize the set of Holder potentials with unique
equilibrium state.

Speaker:

Rene Conijn (Utrecht)

Title:

Largest clusters in Percolation and Conformal Measure Ensembles

Abstract:

Consider an n x nbox in the triangular lattice. The asymptotic behaviour, as n tends to infinity, of the largest percolation clusters in this box was well studied by Borgs, Chayes, Kesten and Spencer in (1999 and 2001). However some questions remained open. If we restrict ourself to critical percolation the size of the largest cluster is of the order n^(91/48). The first natural question is: does there exist a limiting distribution for the size of the largest cluster scaled by its order? In this talk we discuss the existence of the limiting distribution and introduce conformal measure ensembles as a key ingredient. Furthermore we will see an interesting application of these measure ensembles to the FKIsing model. Based on joint work with Rob van den Berg, Federico Camia and Demeter Kiss.

Speaker:

Christoph HoferTemmel (NLDA Den Helder)

Title:

Disagreement percolation for the hardsphere model

Abstract:

We study uniqueness conditions for the Gibbs measure of the
hardsphere model on $R^d$ in the the high temperature case. Classic sufficient conditions for uniqueness in the hightemperature case are cluster expansions and Dobrushin's uniqueness criterion. We generalize
disagreement percolation, another sufficient condition, from the lattice
case to the point process case. Disagreement percolation, introduced by
Maes and van den Berg, compares the competing influence of different boundary conditions for finite volume specifications with a product field and then uses percolation bounds on the product field to derive the uniqueness of the Gibbs measure. Using the same approach together with bounds on the percolation threshold of the Boolean disc model, we derive lower bounds on the extent of the uniqueness region of the infinite volume Gibbs measure.
The key tools are a dependent, recursive and simultaneous thinning of a Poisson point process to several dominated point processes and a concept of densities of couplings of simple point processes. For every finite volume and all choices of boundary conditions, we are able to stochastically dominate two instances of the hardsphere model with these boundary conditions at a given activity simultaneously by a Poisson point process of the same activity. The resulting disagreement percolation bounds are better than the theoretically best possible lower bounds by cluster expansion techniques. I close with a list of possible extensions and an outlook of future work around marked Gibbs point processes.

Speaker:

Federico Camia (NYU Abu Dhabi)

Title:

From Brownian Loops to Conformal Fields

Abstract:

The study of lattice fields is an important topic in statistical
mechanics and modern probability theory. In various two dimensional
models that undergo a continuous phase transition, when a continuum
scaling limit is performed (i.e., when the lattice spacing is sent to
zero) at the critical point, such lattice fields are known or believed
to converge to continuum fields endowed with a type of symmetry called
conformal invariance. The prototypical example is the spin field in
the critical, twodimensional Ising model.
In this talk, I will discuss a class of conformal fields constructed
out of planar Brownian loops via a cutoff procedure. The goal is to
highlight the main features of the continuum scaling limit and of the
emergence of conformal fields within a class of models where both
conceptual and technical issues are relatively transparent and easy to
treat.
(The models I will describe are actually motivated by cosmology, and
seem to lead to conformal field theories with novel features, but I
will not focus on those aspects in this talk. No prior knowledge of
conformal field theory will be assumed. The talk is based on joint
work with Alberto Gandolfi and Matthew Kleban: Conformal correlation
functions in the Brownian loop soup, Nuclear Physics B 902 (2016),
483507.)

Speaker:

David Coupier (Universite Lille 1)

Title:

Navigation on Geometric Random Graphs

Abstract:

In this talk, we consider three models of Geometric Random Graphs which are defined in a very similar way. Their vertex sets are given by a Poisson point process (in the euclidean plane) and their graph structures obey to the same geometric rule. In fact, only their directions differ. The first one is radial and has been introduced by F. Baccelli and C. Bordenave in 2005 to model telecommunications networks. The second one is directed according to a given vector whereas the third one has no favorite directions. We will study the number of topological ends for these three models.

Speaker:

Willem van Zuijlen (Leiden)

Title:

Meanfield GibbsnonGibbs transitions

Abstract:

In this talk I discuss dynamical GibbsnonGibbs transitions for meanfield spin systems. Gibbsianness is related to the number of global minimisers of a large deviation rate function. A unique global minimiser implies Gibbsianness while multiple imply nonGibbsianness. I explain the background of this relation and list possible scenarios when the spins perform independent Brownian motions.
This is joint work with Frank den Hollander and Frank Redig.

Speaker:

Matej Stehlik (Université Grenoble Alpes)

Title:

Topological bounds on the chromatic number

Abstract:

Topological bounds on the chromatic number of graphs originate from
Lovasz’s celebrated proof of Kneser’s conjecture in 1977. The general
idea is to associate a simplicial complex to a graph, and then to
bound the chromatic number of the graph in terms of certain
topological invariants of the associated complex.
In this talk, we will explore an alternative approach using what we
call higherdimensional projective quadrangulations. We will
illustrate this on some classes of graphs such as Kneser graphs, and
also show how one of the “classical" topological bounds can be
expressed purely in terms of projective quadrangulations.
This is joint work with Tomas Kaiser.

Speaker:

Alessandra Cipriani (WIAS Berlin)

Title:

The Membrane model

Abstract:

The membrane or bilaplacian model was first introduced in the physics
literature to model random interfaces with constant curvature, and studied
mathematically for the first time by Sakagawa and Kurt. It is a centered
multivariate Gaussian whose covariance is given by the discrete
bilaplacian operator on the lattice. It is tempting to think of it as a
kin of the discrete Gaussian free field (GFF), and indeed many results can
be deduced with the same methods for both, as for example
the fluctuations of the maximum in higher dimensions. Moreover, as the GFF,
it also can be seen as a generalised Gaussian variable arising as scaling
limit of discrete models, for example in the odometer of the divisible
sandpile or height fluctuations in uniform spanning forest. We will
discuss some of the interesting features of the model and some open
conjectures.
The talk is an overview of the area and should be accessible to everybody.
Based on joint works with Alberto Chiarini, Rajat Subhra Hazra and Wioletta Ruszel.

Speaker:

Moumanti Podder (NYU)

Title:

The strange logic of GaltonWatson trees

Abstract:

This talk will focus on probabilities of first order (FO) and existential monadic second order (EMSO) sentences on the GaltonWatson (GW) tree.
I shall limit myself to Poisson offspring distributions, though many of the results can be extended to very general distributions.
Fix $k \in \mathbb{N}$. Conditioned on survival of the tree, we show that all FO sentences of quantifier depth $k$ are determined by a local
neighbourhood of the root (of radius $\approx 3k+2$). We devise a recursive procedure to compute these probabilities, conditioned on the
tree’s survival. The probabilities are very nice functions of $\lambda$ and $p \lambda$, the survival probability. Using Ehrenfeucht games and
corresponding equivalence classes, we show that the probability of any FO sentence is analytic in $\lambda$.
I shall discuss some of our ongoing work: rogue solutions, i.e. solutions of equations derived from tree automata that do not admit any interpretation; an example of a sentence that is not expressible almost surely as an EMSO, etc. I shall end with speculations and conjectures that hopefully the audience will find fascinating.
Parts of this are joint work with Joel Spencer, Alexander Holroyd, Yuval Peres, Tobias Johnson, Fiona Skerman, Avi Levy.

Speaker:

Mathew Penrose (Bath, UK)

Title:

The strong giant in a random digraph

Abstract:

Consider a random directed graph on n vertices
with outdegrees sampled independently at random
from an arbitrary specified probability distribution
on the nonnegative integers, and
destinations of arcs selected independently and
uniformly at random. We say two vertices lie
in the same strong component if they intercommunicate.
We discuss the emergence of a unique giant component
for large n, provided the mean outdegree exceeds 1.
Time permitting, we discuss related results for
other random graph models.

Speaker:

Johan van Leeuwaarden (TU/e)

Title:

Solvable random network model for disordered sphere packings in all dimensions

Abstract:

A notorious open problem in physics is to create a solvable model for random sequential adsorption (RSA) of nonoverlapping spheres in continuum spaces for dimensions 2 and higher. In its simplest form, spheres arrive sequentially at uniformly chosen locations in space and are deposited when there is no overlap with a previously deposited sphere. Due to the spatial correlation, characterizing the fraction of accepted spheres or the area covered by the deposited spheres, becomes intractable after a large number of deposition attempts.
We investigate such disordered packings of spheres by taking a novel approach that compares continuum RSA with nearestneighbor blocking on a sequence of clustered random networks with a growing number of vertices. This tractable network model leads to a precise characterization of coverage, including formulas for ensemble averages and fluctuations. We discover laws that describe the packing fraction as a function of density and dimension. By investigating the spatial dimensions two to five over wide density ranges, we show that these laws are universal.
The network model advances the theoretical study of higherdimensional disordered packings and has several potential applications, including the dipoleblockade of ultracold Rydberg gas molecules, studied for their potential impact on quantum computing. The predictions from the model also confirm the widely observed subPoissonian nature (variance to mean ratio well below one) of disordered packings, and support the conjectured lower bounds on the optimal sphere packings in high dimensions.
This is joint work with Souvik Dhara and Debankur Mukherjee. We also discuss recent joint work with Clara Stegehuis and Remco van der Hofstad on hierarchical random graphs and recent works of among other Jaron Sanders and Svante Janson on jamming limits for random graphs.

Speaker:

Maria Remerova (UvA)

Title:

Queueing systems with random fluid limits

Abstract:

Fluid limits are lawoflargenumbers type of limits, and as such, they are usually deterministic. In this talk, I will present two queueing models that have random fluid limits: a polling model in overload and a model inspired by synchronization processes in the Bitcoin network.

Speaker:

Arnoud den Boer (UvA)

Title:

Decisionbased model selection

Abstract:

In datadriven optimization problems, simple mathematical models that discard important factors may sometimes be preferred to more realistic models. This may occur if the parameters of the simple model are easier to estimate than the parameters of the complex model, or if the optimization problem corresponding to the simple model can be solved exactly whereas the optimization problem corresponding to the `realistic model' is intractable. This tradeoff between three sources of errors (modeling, estimation, and optimization errors) is encountered in many stochastic optimization problems.
The question we address is: how can one determine if it is better to use a simplified model, rather than a more realistic model? In other words: given a particular optimization problem and a data set at hand, how do we know whether the modelmisspecification error of a simple model is dominated by estimation and optimization errors of more realistic models?

Speaker:

Luca Avena (Leiden)

Title:

RW kernels, spanning forests and multiscale analysis on graphs.

Abstract:

We use ideas from largescale stochastic dynamics to build a multiresolution scheme to analyse arbitrary functions on graphs. These types of problems emerge naturally in the context of signal processing. The goal is to obtain successive approximations at different scales of arbitrary functions on graphs which are used for signal classification, reconstruction and data compression. When the signal is defined on a graph having enough regularity structures, several methods (such as wavelets) are available in the literature and used in practice. When the regularity structure of the graph is lacking, very few methods are known. Our work aims at addressing this issue by using random spanning forests, looperased walks, determinantal structures, random walk kernels and intertwining of Markov chains.
Joint work with Castel, Gaudilliere and Melot.

Speaker:

Francesca Collet (Delft)

Title:

Selfsustained oscillations in dissipative mean field interacting particle systems

Abstract:

An important issue in Complex Systems is to understand how many interacting units organize to produce “coherent” behavior at macroscopic level. Basic examples include polarization (e.g. spin alignments in Isinglike models) and synchronization (e.g. phase locking in interacting rotators). In this talk we deal with a different, and less understood, phenomenon of selforganization: the emergence of periodic behavior in systems whose units have no tendency to evolve periodically.
We will show how the interplay between dissipation and noise can be responsible for selfsustained oscillations in some mean field interacting particle systems.
This talk is based on joint work with Paolo Dai Pra and Marco Formentin.

Speaker:
 Reem Yassawi (Trent University, Canada)

Title:
 Random orders on Bratteli diagrams 
Abstract:

The FisherWright model describes gene survival in a variable size population, giving conditions for gene heterogeneity as a function of population growth. We recreate this model in the context of BratteliVershik dynamical systems} $(X,T)$. Bratteli diagrams were first studied in operator algebras, and provide partial information about the dynamical system under consideration. Complete information is given by the order imposed on the Bratteli diagram. In our setting the FisherWright model describes the nature of the resulting dynamical system, and gives us the dichotomy: a random order on a slowly growing Bratteli diagram admits a homeomorphism, while a random order on a quickly growing Bratteli diagram does not. This is joint work with Jeannette Janssen and Anthony Quas. The talk is aimed at an audience with only elementary knowledge of probability theory!

Speaker:
 Reka Szabo (Groningen)

Title:
 From survival to extinction of the contact process by the removal of a single edge 
Abstract:

The contact process is one of the most wellstudied stochastic models of the spread of epidemics on a graph, and can also be seen as a continuoustime version of oriented percolation. Its behaviour can be affected by local modifications in the underlying graph. In this talk I will give a construction of a tree in which the contact process with any positive infection rate survives but, if a certain privileged edge is removed, one obtains two subtrees in which the contact process with infection rate smaller than 1/4 dies out.

Speaker:
 Karma Dajani (Utrecht)

Title:
 Invariant measures, matching and the frequency of 0 for signed binary expansions 
Abstract:

We introduce a parametrized family of maps $S_{\alpha}$, the so called symmetric doubling maps, defined on $[1,1]$ by $S_{\alpha}(x)=2xd\alpha$, where $d\in \{1,0,1 \}$ and $\alpha\in [1,2]$. Each map $S_\alpha$ generates binary expansions with digits 1,0 and 1. The transformations $S_{\alpha}$ have a natural invariant measure $\mu_{\alpha}$ that is absolutely continuous with respect to Lebesgue measure. We show that for a set of parameters of full measure, the invariant measure of the symmetric doubling map is piecewise smooth. We also study
the frequency of the digit 0 in typical expansions, as a function of the parameter $\alpha$. In particular, we investigate the self similarity displayed by the function $\alpha\to \mu_{\alpha}([1/2,1/2]$, where
$\mu_{\alpha}([1/2,1/2]$ denotes the measure of the cylinder where digit zero occurs.
This is joint work with Charlene Kalle.

Speaker:
 Derong Kong (Leiden)

Title:
 On the bifurcation set of unique Expansions 
Abstract:

Expanding a real number in a noninteger base is an interesting topic in mathematics. Most notably it has close
connection with dynamical systems, number theory and fractal geometry. Following the works of Paul Erdos and Vilmos Komornik in the 1990s
we investigated the geometrical properties of unique expansions in a noninteger base as well as the set of bases for which 1 has a unique expansion.
This is a joint work with Kalle, Li and Lu.

Speaker:
 Sandjai Bhulai (VU Amsterdam)

Title:
 Value Function Discovery In Markov Decision Processes 
Abstract:

In this talk, we introduce a novel method for discovery of value functions for Markov Decision Processes (MDPs). This method is based on ideas from the evolutionary algorithm field. Its key feature is that it discovers descriptions of value functions that are algebraic in nature. This feature is unique, because the descriptions include the model parameters of the MDP. The algebraic expression can be used in several scenarios, e.g., conversion to a policy, control of systems with timevarying parameters. We illustrate its application on an example MDP.

Speaker:
 Matej Stehlik (Université Grenoble Alpes)

Title:
 Edge and facewidth of projective quadrangulations 
Abstract:

Graphs which embed in the projective plane so that all faces are bounded by four edges are called projective quadrangulations. They are a fascinating class of graphs with some surprising properties. In this talk, we will give upper bounds on the edgewidth and the facewidth of nonbipartite projective quadrangulations. The former is sharp, while the latter is a constant away from the optimal. We will also discuss some related questions.
Joint work with Louis Esperet

Speaker:
 Sandór Kolumbán (TU/e)

Title:
 Criticality in the brain, what we can and cannot see 
Abstract:

Classical dynamical models (like the Ising model) have very different behavior in their sub, super and critical phase and this is universal to some extent. A large amount of empirical evidence shows that brain functionality resembles this universal behavior around criticality.
During this presentation we will briefly overview some of the empirical evidence supporting that the brain is a system around criticality. We will also try to go beyond directly measurable properties of the brain based on this insight of criticality.
A version of the Ising model is introduced that captures particular aspects of the brain behavior. Examining this model around criticality boils down to classical results in some cases but its behavior is suspected to be different in other cases. We will discuss some open questions related to this model.
This is ongoing joint work with Remco van der Hofstad and Julia Komjáthy.

Speaker:
 Wioletta Ruszel (TU Delft)

Title:
 Longrange Ising models: phase transitions and interfaces 
Abstract:

Longrange models are very special since they allow a phase transition to occur even in 1d lattice models which is in general not possible for ordinary spin models.
Even more surprising, this phenomenon persists in the presence of fields which usually “stear” a spin model towards a certain preference in phase.
In this talk we will first review some recent results on phase transition phenomena of 1d longrange Ising models with external fields, announced in [1]. In the second part we will discuss some work in progress concerning Dobrushin interfaces and its fluctuations. A Dobrushin interface is a separation line which appears when the lattice is conditioned to be in one phase in one half of the lattice and in the other phase on the other half. For shortrange models this has been done for example using the relation between Ising models and percolation. There is also a corresponding FortuinKasteleyn representation for longrange models and we are trying currently to extend the analysis for the longrange case.
This is joint work with:
Rodrigo Bissacot (Sao Paolo), Eric Endo (Sao Paolo), Aernout van Enter (Groningen), Bruno Kimura (Delft), Arnaud Le Ny (Paris),
[1] Dyson models under renormalization and in weak fields
R. Bissacot, E.O. Endo, A.C.D. van Enter, B. Kimura, A. Le Ny, W.M. Ruszel
arXiv:1702.02887, 2017

Speaker:
 Pieter Trapman (Stockholm U.)

Title:
 End of an SIR epidemic on a configuration model network 
Abstract:

We consider an SIR (SusceptibleInfectiveRecovered) epidemic on a
static (configuration model) random graph. We describe the final stages
of the epidemic and analyse the time until extinction of the epidemic.
Furthermore, we consider the effect of control measures, such as
vaccination on the duration of the epidemic. The analysis heavily relies
on theory on branching processes.
We show that the epidemic is always exponentially declining in the final
stages, even if the degree distribution of the network has infinite
variance. We also show that control measures, although
decreasing the size of the epidemic, might well increase the duration of
the epidemic, which might have serious public health and economic
implications.
Joint work with Ana Serafimovic and Abid Ali Lashari


