This talk presents precise large deviation asymptotics (Bahadur-Rao type) for the total population in a multitype branching process within an i.i.d. random environment. The offspring law is environment-dependent. Our method combines a martingale argument with a Cramér-type change of measure, under which we prove stable convergence for products of random matrices and L^pconvergence for the branching process. The results rely on precise large deviation theory for random matrices. (Joint work with Ion Grama and Thi Trang Nguyen)

Speaker's profile: Liu Quansheng, a French distinguished professor, works at the University of South Brittany and enjoys the French Excellent Research Allowance (PES/PEDR). I enrolled in the Mathematics Department of Wuhan University in 1980 and obtained my undergraduate and master's degrees in 1984 and 1987, respectively; In 1989, he went to France for further studies and obtained a doctoral degree in probability theory from the University of Paris VI (now Sorbonne University) in 1993. From 1993 to 2000, he served as a lecturer and associate professor at the University of Rennes in France. Since September 2000, he has been a professor at the University of South Brittany in France. Long term head of the Mathematics Department at the University of South Brittany (Directeur du Laboratoire de Math é matiques). Collaborated with a colleague from the University of Brest to establish the Laboratoire de Math é matiques de Bretagne Atlantique (CNRS UMR6205) directly under the French research center. The leader has established the Third Stage Diploma in Applied Mathematics (DESS) and the Master's Diploma in Mathematics and Applied Mathematics, and has been responsible for the long-term training of graduate students in mathematics and applied mathematics.

Professor Liu Quansheng's research topic involves probability statistics, fractal geometry, and digital image processing. In recent years, the main focus of research has been on probability and statistical problems in stochastic environments, particularly in the areas of large deviation theory, random matrix multiplication, and several important mathematical, physical, and applied probability models for stochastic environments, including branching processes, branching random walks, and image denoising. Published over 100 papers in journals such as J. Eur. Math. Soc., Annals of Probability, Probab. Th. Rel. Fields, Annals of Applied Probability, IEEE Trans. Image Processing, etc.