时间: 2025年3月27日（周四）15:00开始

地点: 东区第五教学楼5101

报告1：

题目: Quasi-Stationary Distributions

报告人: 易英飞（University of Alberta & Jilin University）

摘要: Quasi-stationary distributions (QSDs) are those almost invariant to a diffusion process over exponentially long time. Representing important transient stochastic dynamics, they arise frequently in applications especially in chemical reactions and population systems admitting extinction states. This talk will present some rigorous results on the existence, uniqueness, concentration, and convergence of QSDs along with their connections to the spectrum of the Fokker-Planck operator.

报告2：

题目: Existence and regularity of the quasi-potential function in LDP

报告人:亓维维，中科院数学与系统科学研究院

摘要: Real systems are often subject to noises due to internal uncertainties and complexity as well as external randomness. Even small noises can lead to intriguing dynamics across multiple timescales including transient dynamics and long-term dynamics captured by quasi-stationary distributions and stationary distributions, respectively. Understanding the asymptotic behaviors of (quasi-)stationary distributions in the small noise limit is of fundamental importance. However, this analysis presents a singular limit, posing significant challenges. A powerful approach is to establish the large deviation principle (LDP) for (quasi-)stationary distributions. In this talk, we will present our recent results on the existence and regularity of the quasi-potential function in LDP, which have broad and impactful applications across various disciplines. Specifically, we will discuss its applications in non-equilibrium thermodynamics.