报告摘要：We study random walks on the general linear group constrained to a specific domain, with a focus on their asymptotic behavior. We first construct the target harmonic measure, a key element in formulating the local limit theorem for conditioned random walks on groups. The main challenge arises from analyzing the conditioned reverse walk, whose increments, in the context of random walks on groups, depend on the entire future trajectory. To address this, we introduce a reversed sequence characterized as a dual random walk perturbed by future observations, and develop an approach based on the finite-size approximation of these perturbations. Combining a Caravenna-type conditioned local limit theorem with a conditioned central limit theorem for the reversed walk, we then establish the local limit theorem for conditioned 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-François Quint.

个人简介：肖惠，中国科学院数学与系统科学研究院副研究员，入选国家海外高层次青年人才计划（青年项目）。研究方向为概率论，主要包括随机矩阵乘积的极限理论、群上的分枝随机游动等。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, J. Theoret. Probab., Sci. China Math.等

报告时间：2025年6月7日8：30 -11：30

报告地点：北衡楼1420