Abstract

Three lectures are planned to present some recent limit theorems for products of independent and identically distributed random matrices, and related topics. We focus on precise large deviations and convergence rates in the Gaussian approximation, and applications to multi-type branching processes in random environments, branching random walks, and Mandelbrot’s cascades.

Speaker

Quansheng Liu is professor of exceptional class at University of South Brittany (Univ. Bretagne-Sud, France). From 2007 to 2013 and from 2017 to 2022, he has been the Director of the Laboratory of Mathematics of University of South Brittany, and Associate Director of the Laboratory of Mathematics of Atlantic Brittany. He received his B.S. and M.S. degrees in Mathematics from Wuhan University respectively in 1984 and 1987, and his Ph.D. degree in Probability from University Paris 6 in 1993. His research interests include probability theory and image processing. He has published over 100 research articles in scientific journals, such as J. Eur. Math. Soc., Prob. Th. Rel. Fields, Ann. Prob., Ann. Appl. Prob., IEEE Trans. Image Processing, SIAM J. Imaging Sciences, and J. Sci. Comput. , etc.