Universiteit Utrecht

Department of Mathematics


Curl-free walks in Z 2 and the lamplighter problem



Cédric Boutillier (CWI)
23 May 2006

A curl-free walk in Z 2 is a closed path crossing every edge the same number of times in both directions. A natural question is : what is the number of such walks on length  n ? After giving a method to solve this problem, we will apply it to a toy-model and explain the connections with other objects, such that the Schrödinger equation with random potential, or the lamplighter group.


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Yuri Yakubovich