In this short talk, I will first introduce the celebrated Marcenko-Pastur discovered half century ago for the Wishart matrix enemble. Then modern extensions are introduced firstly when the matrix entries have an infinite second moment (like Cauchy random varaibles); and secondly, when matrices are replaced by large-dimensional tensors.
Professor Yao worked as an Assistant/Associate Professor in the University of Paris I Panthéon-Sorbonne from 1990 to 2000. From 2000, he has been a Full Professor of applied mathematics in the University of Rennes 1. He also held visiting positions at SUDIMAGE R&D from 1989-1994, and at INRIA, France from 2003-2004. From 2015, he worked at the University of Hong Kong as a Full Professor. Professor Yao is an international leading scholar in random matrix theory and high-dimensional statistics. His book Large Sample Covariance Matrices and High-Dimensional Data Analysis (Cambridge University Press, 2015, co-authored with Zhidong Bai and Shurong Zheng) is an authoritative reference of the field. He was elected as a Fellow of the Institute of Mathematical Statistics (U.S.A.) with the citation: “For influential contribution to the inferential aspects of random matrix theory in the analysis of high-dimensional data”.