Existence and regularity of the quasi-potential function in LDP
Time: 2025-10-15
Published By: Qiuye Huang
Speaker(s): Weiwei Qi (AMSS, CAS)
Time: 16:00-17:00 October 23, 2025
Venue: Room 29, Quan Zhai, BICMR
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, I 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.
