Metastability and Multiscale Extinction Time on a Finite System of Interacting Stochastic Chains

Описание: Next Wednesday, March 25 2026, at 2:00 pm, Miguel Abadi - Departamento de Estatística – IME - USP, will give a talk in our seminar.

Title: Metastability and Multiscale Extinction Time on a Finite System of Interacting Stochastic Chains

Abstract: We investigate the metastability and extinction time of a finite discrete- time system composed of a large number of interacting components. The system is Markovian with respect to the potential profiles of the components, which are simultaneously subject to leakage and gain effects. We show that the only invariant measure is the null configuration and that it is reached in finite time. Additionally, the system exhibits a metastable state and a metastable barrier, which governs the timescale of the system’s lifetime. We identify a critical parameter, below which the extinction time is independent of system size. Above this critical value, the extinction time depends on the number of components, exhibiting infinitely many scaling behaviors governed by a nontrivial relationship among leakage, gain, and system size.