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- W2015204328 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." @default.
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- W2015204328 date "2011-01-01" @default.
- W2015204328 modified "2023-10-16" @default.
- W2015204328 title "Geometry of the random interlacement" @default.
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- W2015204328 doi "https://doi.org/10.1214/ecp.v16-1660" @default.
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