Holder： Benoît Collins（Kyoto University）
Time：2026-05-18 14:00-15:00
Location：Siyuan Lecture Hall，Zhi Hua Building-225
Abstract:
We consider expectations of the form E[tr h₁(X₁𝑁)⋯tr h𝑟(X𝑟𝑁)], where X𝑖𝑁 are self-adjoint polynomials in various independent classical random matrices and h𝑖 are smooth test functions, and obtain a large N expansion of these quantities, building on the framework of polynomial approximation and Bernstein-type inequalities recently developed by Chen, Garza-Vargas, Tropp, and van Handel. As applications of the above, we prove the higher-order asymptotic vanishing of cumulants for smooth linear statistics, establish a Central Limit Theorem, and demonstrate the existence of formal asymptotic expansions for the free energy and observables of matrix integrals with smooth potentials. This talk is based on joint work with Manasa Nagatsu.
About the Speaker:
Benoît Collins is a Professor in the Department of Mathematics at Kyoto University, Japan. He received his PhD from Université Pierre et Marie Curie (Paris 6) in 2003, following studies at the École Normale Supérieure (Paris). Before joining Kyoto University in 2014, he held permanent positions at CNRS (Université Lyon 1) and the University of Ottawa. His research spans random matrix theory, free probability, operator algebras, and quantum information theory. He was an invited speaker at the International Congress of Mathematicians (ICM 2022). He is the recipient of the JSPS Prize (2022), the Autumn Prize of the Mathematical Society of Japan (2023), the Frontiers of Science Award of the International Congress of Basic Science (ICBS, Beijing, 2025), and the Commendation for Science and Technology by the Minister of Education, Culture, Sports, Science and Technology of Japan (MEXT, 2025).
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