Open Access
March 2017 A lower bound for disconnection by simple random walk
Xinyi Li
Ann. Probab. 45(2): 879-931 (March 2017). DOI: 10.1214/15-AOP1077


We consider simple random walk on $\mathbb{Z}^{d}$, $d\geq3$. Motivated by the work of A.-S. Sznitman and the author in [Probab. Theory Related Fields 161 (2015) 309–350] and [Electron. J. Probab. 19 (2014) 1–26], we investigate the asymptotic behavior of the probability that a large body gets disconnected from infinity by the set of points visited by a simple random walk. We derive asymptotic lower bounds that bring into play random interlacements. Although open at the moment, some of the lower bounds we obtain possibly match the asymptotic upper bounds recently obtained in [Disconnection, random walks, and random interlacements (2014)]. This potentially yields special significance to the tilted walks that we use in this work, and to the strategy that we employ to implement disconnection.


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Xinyi Li. "A lower bound for disconnection by simple random walk." Ann. Probab. 45 (2) 879 - 931, March 2017.


Received: 1 January 2015; Revised: 1 September 2015; Published: March 2017
First available in Project Euclid: 31 March 2017

zbMATH: 06797082
MathSciNet: MR3630289
Digital Object Identifier: 10.1214/15-AOP1077

Primary: 60F10 , 60K35
Secondary: 60J27 , 82B43

Keywords: large deviations , Random interlacements , Random walk

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 2 • March 2017
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