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

报 告 人：肖惠 副研究员 （中国科学院数学与系统科学研究院）

报告时间：5月26日（周五）10:00- 11:00

腾讯会议：625-908-014(10:00- 10:30)，665-531-709(10:30- 11:10)

报告摘要：Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. In this talk, we show how to construct the target harmonic measure, which, together with the harmonic function, serves as a pivotal component in shaping the conditioned local limit theorem. Using a reversal identity, we introduce a reversed sequence characterized as a dual random walk with a perturbation depending on future observations. The investigation of such walks, which rely on future information, lies at the heart of the research. To carry out this study, we develop an approach based on the finite-size approximation of perturbations, enabling us to simplify the investigation to an array of Markov chains with increasing dimensions.

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，入选国家海外高层次人才计划。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。