Sharp asymptotics of disconnection time of large cylinders by simple and biased random walks

2024/09/26 by Li, Xinyi, Liu, Yu, Wang, Yuanzheng
#60G50 #60K35 #82C41 (Primary) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2409.17900

Abstract

We investigate the asymptotic disconnection time of a large discrete cylinder (ℤ/Nℤ)^d× ℤ, d≥ 2, by simple and biased random walks. For simple random walk, we derive a sharp asymptotic lower bound that matches the upper bound from [Sznitman, Ann. Probab., 2009]. For biased walks, we obtain bounds that asymptotically match in the principal order when the bias is not too strong, which greatly improves non-matching bounds from [Windisch, Ann. Appl. Probab., 2008]. As a crucial tool in the proof, we also obtain a "very strong" coupling between the trace of random walk on the cylinder and random interlacements, which is of independent interest.

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