报告题目：Conditioned random walks on the general linear group.

报告摘要：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.

报告人姓名：肖惠

报告人所在单位：中国科学院数学与系统科学研究院

报告人职称：副研究员

报告时间：2025年6月14日（星期六）下午15:00-16:00

报告地点：理科楼A212

报告人简介：肖惠，中国科学院数学与系统科学研究院副 研究员。研究方向为概率论，主要包括随机矩阵乘积的极 限理论、群上分枝随机游动等。相关论文发表在 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.