RECURRENCE OF EDGE-REINFORCED RANDOM WALK ON A TWO-DIMENSIONAL GRAPH

By F. Merkl, Silke W. W. Rolles. 2007

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We consider a 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 the linearly edge-reinforced random walk on these graphs is recurrent. Furthermore, we derive bounds for the probability that the edge-reinforced random walk hits the boundary of a large box before returning to its starting point.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fa42ebaf138a7d5ceff6ab132bd8a2c06eb08972