Open Access
2012 On the internal distance in the interlacement set
Jiří Černý, Serguei Popov
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Electron. J. Probab. 17: 1-25 (2012). DOI: 10.1214/EJP.v17-1936


We prove a shape theorem for the internal (graph) distance on the interlacement set $\mathcal{I}^u$ of the random interlacement model on $\mathbb Z^d$, $d\ge 3$. We provide large deviation estimates for the internal distance of distant points in this set, and use these estimates to study the internal distance on the range of a simple random walk on a discrete torus.


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Jiří Černý. Serguei Popov. "On the internal distance in the interlacement set." Electron. J. Probab. 17 1 - 25, 2012.


Accepted: 12 April 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1245.60090
MathSciNet: MR2915665
Digital Object Identifier: 10.1214/EJP.v17-1936

Primary: 60K35
Secondary: 60G50 , 82B43

Keywords: capacity , Internal distance , Random interlacement , shape theorem , Simple random walk

Vol.17 • 2012
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