The Annals of Probability
- Ann. Probab.
- Volume 37, Number 5 (2009), 1679-1714.
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 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.
Ann. Probab., Volume 37, Number 5 (2009), 1679-1714.
First available in Project Euclid: 21 September 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60K37: Processes in random environments
Merkl, Franz; Rolles, Silke W. W. Recurrence of edge-reinforced random walk on a two-dimensional graph. Ann. Probab. 37 (2009), no. 5, 1679--1714. doi:10.1214/08-AOP446. https://projecteuclid.org/euclid.aop/1253539854