How universal are asymptotics of disconnection times in discrete cylinders?

Abstract

We investigate the disconnection time of a simple random walk in a discrete cylinder with a large finite connected base. In a recent article of A. Dembo and the author it was found that for large $N$ the disconnection time of $G_N\times \mathbb{Z}$ has rough order $|G_N{|}^2$, when $G_N=(\mathbb{Z}/N\mathbb{Z}{)}^d$. In agreement with a conjecture by I. Benjamini, we show here that this behavior has broad generality when the bases of the discrete cylinders are large connected graphs of uniformly bounded degree.

arXiv commentPublished in at http://dx.doi.org/10.1214/009117907000000114 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (14)

• Decoupling inequalities and interlacement percolation on G x Z
• Upper bound on the disconnection time of discrete cylinders and random interlacements
• Geometry of Gaussian free field sign clusters and random interlacements
• Random interlacements and amenability
• Diffusion Limited Aggregation on a Cylinder
• Percolation Perspective on Sites Not Visited by a Random Walk in Two Dimensions
• On the disconnection of a discrete cylinder by a biased random walk
• Cover times in the discrete cylinder
• Percolation of sites not removed by a random walker in $d$ dimensions
• Percolation for the Vacant Set of Random Interlacements
• Random walks on discrete cylinders with large bases and random interlacements
• Random Walks on Discrete Cylinders and Random Interlacements
• Interlacement percolation on transient weighted graphs
• Intersection exponents for biased random walks on discrete cylinders