Abstract:
In this talk, we will present some recent findings on two seemingly unrelated topics: the law of fractional logarithm for the Wigner minor process, and the numerical radius of non-Hermitian random matrices. The former can be regarded as an analogue, for the largest eigenvalue of Wigner matrices, of the classical law of the iterated logarithm, while the latter concerns the extremal Rayleigh quotients of non-Hermitian random matrices. Ultimately, both questions reduce to the study of the extrema of an Airy-like process over long time periods, where a correlation–decorrelation transition in this process becomes the key to the analysis. This talk is based on joint research with Giorgio Cipolloni, László Erdős, Joscha Henheik, and Oleksii Kolupaiev.
About the Speaker:
Prof. Zhigang Bao received his PhD from Zhejiang University in 2013 and held postdoctoral positions at Nanyang Technological University and IST Austria from 2013 to 2016. He joined HKUST in 2016, and since 2024 he has been an Associate Professor at the University of Hong Kong. His research focuses on Random Matrix Theory, Free Probability Theory, and their applications in high-dimensional statistics.
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