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2011 Geometry of the random interlacement
Eviatar Procaccia, Johan Tykesson
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Electron. Commun. Probab. 16: 528-544 (2011). DOI: 10.1214/ECP.v16-1660

Abstract

We consider the geometry of random interlacements on the $d$-dimensional lattice. We use ideas from stochastic dimension theory developed in [1] to prove the following: Given that two vertices $x,y$ belong to the interlacement set, it is possible to find a path between $x$ and $y$ contained in the trace left by at most $\lceil d/2 \rceil$ trajectories from the underlying Poisson point process. Moreover, this result is sharp in the sense that there are pairs of points in the interlacement set which cannot be connected by a path using the traces of at most $\lceil d/2 \rceil-1$ trajectories.

Citation

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Eviatar Procaccia. Johan Tykesson. "Geometry of the random interlacement." Electron. Commun. Probab. 16 528 - 544, 2011. https://doi.org/10.1214/ECP.v16-1660

Information

Accepted: 26 September 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1254.60018
MathSciNet: MR2836759
Digital Object Identifier: 10.1214/ECP.v16-1660

Subjects:
Primary: Probability

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