Existence and regularity of the quasi-potential function in LDP

Speaker: 亓维维 中科院应数所

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

Inviter: 随机分析研究中心

Time & Venue: 2025 年7月4日15:00–16:00 南楼613

Abstract: 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.