Manasa Nagatsu: Large $N$ expansion for smooth multi-trace spectral statistics of classical matrix ensembles, central limit theorems and matrix integrals.

mercredi 25 févr. 2026, 14:00 → 15:00 Europe/Paris

We consider expectations of the form $E [tr h_1(X_1^N)... tr h_r(X_r^N)]$, where $X_i^N$ are self-adjoint polynomials in various independent classical random matrices and $h_i$ are smooth test function 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 Benoît Collins.