報告承辦單位：數學與統計學院
報告題目：Conditioned random walks on the general linear group.
報告摘要：We study random walks on the general linear group constrained to a specificdomain, with a focus on their asymptotic behavior. We first construct the target harmonicmeasure, a key element in formulating the conditioned local limit theorem. The main challenge arises from analyzing the conditioned reversed walk, whose increments, in the context of random walks on groups, depend on the entire future trajectory. To address this, weintroduce a reversed sequence characterized as a dual random walk perturbed by futureobservations, and develop an approach based on the finite-size approximation of these perturbations.Combining a Caravenna-type local limit theorem with a conditioned central limit theorem for the reversed walk, we then establish the local limit theorem for random walks on groups. As an application, we derive the exact local behavior of the exit time. This is based on joint work with Ion Grama and Jean-Fran?cois Quint.
報告人姓名：肖惠
報告人所在單位：中國科學院數學與系統科學研究院
報告人職稱：副研究員
報告時間：2025年6月14日（星期六）下午15:00-16:00
報告地點：理科樓A212
報告人簡介：肖惠，中國科學院數學與系統科學研究院副 研究員。研究方向為概率論，主要包括隨機矩陣乘積的極 限理論、群上分枝隨機游動等。相關論文發表在 J.Eur.Math.Soc., Ann.Probab., Ergodic Theory Dynam. Systems, Ann.Inst.Henri Poincaré Probab. Stat., Stochastic Process. Appl., J.Diffcrential Equations, Sci. China Math.等.