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東京確率論セミナー
過去の記録 ～06/03｜次回の予定｜今後の予定 06/04～
| 開催情報 | 月曜日 16:00～17:30 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 佐々田槙子、中島秀太（慶應義塾大学）、星野壮登（東京科学大学）、蛯名真久（東京科学大学） |
| セミナーURL | https://sites.google.com/view/tokyo-probability-seminar23/ |
2026年06月22日(月)
16:00-17:30 数理科学研究科棟(駒場) 126号室
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
永津 愛彩 氏 (京都大学)
Large $N$ expansion for smooth multi-trace spectral statistics of
classical matrix ensembles, central limit theorems and matrix integrals.
15:15〜 ２階のコモンルームでTea timeを行います。ぜひこちらにもご参加ください。
永津 愛彩 氏 (京都大学)
Large $N$ expansion for smooth multi-trace spectral statistics of
classical matrix ensembles, central limit theorems and matrix integrals.
[ 講演概要 ]
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.
