@article{ECP1660,
author = {Eviatar Procaccia and Johan Tykesson},
title = {Geometry of the random interlacement},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {16},
year = {2011},
keywords = {Random Interlacements; Stochastic dimension},
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.},
pages = {no. 47, 528-544},
issn = {1083-589X},
doi = {10.1214/ECP.v16-1660},
url = {http://ecp.ejpecp.org/article/view/1660}}