2011/01/07 by Eviatar B. Procaccia, Procaccia, Eviatar B., Johan Tykesson +1
Computer Science · Mathematics · #FOS: Mathematics #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #math.PR
paper · pdf · doi:10.48550/arxiv.1101.1527
openalex publication_date 2011/01/07 · arxiv created 2011/07/18 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the geometry of random interlacements on the d-dimensional lattice. We use ideas from stochastic dimension theory developed in \citebenjamini2004geometry 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.