On the exact orders of critical value in Finitary Random Interlacements

Abstract

In this paper, we prove the exact orders of critical intensity $u_{\ast }(T)$ in Finitary Random Interlacements (FRI) in ${\mathbb{Z}}^d,d\ge 3$ with respect to the expected fiber length $T$. We show that as $T\to \infty$, $u_{\ast }(T)\sim T^{-1},d\ge 5;$ $u_{\ast }(T)\sim T^{-1}\log T,d=4;$ $u_{\ast }(T)\sim T^{-1/2},d=3.$ Our estimates also give the order of magnitude at which the percolative phase transition with respect to $T$ takes place.

29 pages, 2 figures

References in corpus (1)

• On Chemical Distance and Local Uniqueness of a Sufficiently Supercritical Finitary Random Interlacement