### Edge-reinforced random walk on a two-dimensional graph

Rolles, SWW *(Technische Universität München)*

Friday 19 December 2008, 09:00-10:00

Seminar Room 1, Newton Institute

#### Abstract

We consider linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from Z^2 by replacing every edge by a sufficiently large, but fixed number of edges in series. We prove that linearly edge-reinforced random walk on these graphs is recurrent.

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