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Tokyo Probability Seminar
Seminar information archive ～06/02｜Next seminar｜Future seminars 06/03～
| Date, time & place | Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Makiko Sasada, Shuta Nakajima (Keio Univ.), Masato Hoshino (Science Tokyo), Masahisa Ebina (Science Tokyo) |
2026/06/22
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Manasa Nagatsu (Kyoto University)
Large $N$ expansion for smooth multi-trace spectral statistics of
classical matrix ensembles, central limit theorems and matrix integrals.
We are having teatime from 15:15 in the common room on the second floor. Please join us.
Manasa Nagatsu (Kyoto University)
Large $N$ expansion for smooth multi-trace spectral statistics of
classical matrix ensembles, central limit theorems and matrix integrals.
[ Abstract ]
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.
In addition to presenting these results, we will briefly review the role
of linear statistics in random matrix theory and discuss the motivation
behind the large $N$ expansion framework introduced in the context of
strong convergence.
This talk is based on joint work with Benoit Collins.
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.
In addition to presenting these results, we will briefly review the role
of linear statistics in random matrix theory and discuss the motivation
behind the large $N$ expansion framework introduced in the context of
strong convergence.
This talk is based on joint work with Benoit Collins.
