On Geometries of Finitary Random Interlacements
Speaker
A/Prof. Yuan Zhang
Peking University
Abstract

In this talk, we discuss geometric properties of Finitary Random Interlacements (FRI) $\mathcal{FI}^{u,T}$ in $\mathbf{Z}^d$. We prove that with probability one $\mathcal{FI}^{u,T}$ has no infinite connected component for all sufficiently small fiber length $T>0$, and a unique infinite connected component for all sufficiently large $T$. At the same time, although FRI may not enjoy global stochastic monotonicity with respect to $T$, we prove the existence of a critical $T_c(u)$ for all large $u$. Moreover, we find the chemical distance on the infinite cluster is of the same order as Euclidean distance as well as a local uniqueness result for all sufficiently large $T$. Researches joint with E.B. Procaccia, J. Ye, Y. Xiong，Z. Cai, and X. Han.