The Eyring–Kramers Law for Extinction Time of Contact Process on Stars

In June 2024, I gave an invited talk at KIAS Analysis, PDE & Probability Seminar. I presented a precise estimate for the mean extinction time of the contact process with a fixed infection rate on a star graph. The talk was based on my research advised by Prof. Insuk Seo, and the preprint of my paper can be found on arXiv.

Abstract

In this talk, we present a precise estimate for the mean extinction time of the contact process with a fixed infection rate on a star graph with $N$ leaves. Specifically, we determine not only the exponential main factor but also the sharp sub-exponential prefactor of the asymptotic formula for the mean extinction time as $N \to \infty$, a level of detail previously available only for complete graphs. We achieved these results by estimating the quasi-stationary distribution on non-extinction using special function theory and refined Laplace’s method, and by applying the potential theoretic approach to metastability of non-reversible Markov processes. This novel integration of methodologies provides new insights into the study of the contact process.

Slides

These are the slides for my talk.