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12月1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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