Recurrence of edge-reinforced random walk on a two-dimensional graph
Recurrence of edge-reinforced random walk on a two-dimensional graph
We consider a linearly edge-reinforced random walk on a class of two-dimensional graphs with constant initial weights. The graphs are obtained from ℤ2 by replacing every edge by a sufficiently large, but fixed number of edges in series. We prove that the linearly edge-reinforced random walk on these graphs is …