12-01【张一威】管楼1418 吴文俊数学重点实验室Dynamical Systems Seminar

发布者:万宏艳发布时间:2019-11-26浏览次数:142

报告题目:Spectral gap of sparse bistochastic matrices with exchangeable rows with application to shuffle-and-fold maps

报告人:张一威,华中科技大学

时间:2019年121日(星期天)14:30--15:30

地点:东区管理科研楼1418教室

 

摘要: We consider a random bistochastic matrix of size $n$ of the form $M Q$ where $M$ is a uniformly distributed permutation matrix and $Q$ is a given bistochastic matrix. Under mild sparsity and regularity assumptions on $Q$, we prove that the second largest eigenvalue of $MQ$ is essentially bounded by the normalized Hilbert-Schmidt norm of $Q$ when $n$ grows large. We apply this result to random walks on random regular digraphs and to shuffle-and-fold maps of the unit interval popularized in fluid mixing protocols.

 

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