Session S06 - Interacting Stochastic Systems

Tuesday, July 13, 12:35 ~ 13:10 UTC-3

The time constant of finitary random interlacements

Sarai Hernandez-Torres

Technion, Israel   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The finitary random interlacement $\text{FRI}(u, T)$ is a Poisson point process of geometrically killed random walks on $\mathbb{Z}^d$, with $d \geq 3$. The parameter $u$ modulates the intensity of the point process, while $T$ is the expected path length. Although the process lacks global monotonicity on $T$, $\text{FRI}(u, T)$ exhibits a phase transition. For $T > T^{*}(u)$, $\text{FRI}(u, T)$ defines a unique infinite connected subgraph of $\mathbb{Z}^d$ with a chemical distance. We focus on the asymptotic behavior of this chemical distance and—in particular—the time constant function. This function is a normalized limit of the chemical distance between the origin and a sequence of vertices growing in a fixed direction. In this sense, the time constant function defines an asymptotic norm. Our main result is on its continuity (as a function of the parameters of $\text{FRI}$).

Joint work with Eviatar B. Procaccia (Technion, Israel) and Ron Rosenthal (Technion, Israel).

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