LA Probability Forum

Series: Caltech/UCLA Joint Probability Seminar Series

Continuity of the time constant of finitary random interlacements

Sarai Hernandez-Torres, Instituto de Matemáticas, National Autonomous University of Mexico,

Talk held at UCLA in Math Sciences Room 6627

Finitary random interlacements (FRI) is a Poisson point process of geometrically killed random walks on Z^d, with d ≥ 3. A parameter u > 0 modulates the intensity of the point process, while T > 0 is the expected path length. The model has gained attention because, although it lacks global monotonicity on T, FRI (u, T) exhibits a phase transition.

In the supercritical regime, FRI (u, T) has a unique infinite cluster on which we consider its chemical distance (or graph distance). This talk focuses on the associated time constant. The time constant is a normalized limit of the chemical distance between the origin and a sequence of vertices growing in a fixed direction, defining a deterministic norm. Our main result is its continuity (as a function of the parameters u and T).

This work is joint with Zhenhao Cai, Eviatar Procaccia, Ron Rosenthal and Yuan Zhang.

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