2007/03/31 by Franz Merkl, Silke W. W. Rolles · 1 citation
Computer Science · Mathematics · #Complexity and Algorithms in Graphs #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #math.PR #msc:60K35 #msc:60K37 #msc:82B41
paper · pdf · doi:10.1214/08-aop446
published as Annals of Probability 2009, Vol. 37, No. 5, 1679-1714 · Published in at http://dx.doi.org/10.1214/08-AOP446 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2009/09/01 · arxiv created 2009/09/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.