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.
A seminar from the Classical and Quantum Transport in the Presence of Disorder conference in association with the Newton Institute programme: Mathematics and Physics of Anderson localization: 50 Years After
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