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 GN×ℤ has rough order |GN|2, when GN=(ℤ/Nℤ)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.
"How universal are asymptotics of disconnection times in discrete cylinders?." Ann. Probab. 36 (1) 1 - 53, January 2008. https://doi.org/10.1214/009117907000000114