2016/12/01 by Eviatar B. Procaccia, Yuan Zhang, Procaccia, Eviatar B. +1 · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR
paper · pdf · doi:10.48550/arxiv.1612.00406
32 pages
arxiv created 2016/12/01 · arxiv updated 2016/12/02
We consider connectivity properties of the Branching Interlacements model in ℤd,~d≥5, recently introduced by Angel, Ráth and Zhu in 2016. Using stochastic dimension techniques we show that every two vertices visited by the branching interlacements are connected via at most \lceil d/4\rceil conditioned critical branching random walks from the underlying Poisson process, and that this upper bound is sharp. In particular every such two branching random walks intersect if and only if 5≤ d≤ 8. The stochastic dimension of branching random walk result is of independent interest. We additionally obtain heat kernel bounds for branching random walks conditioned on survival.