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【集中講義】
2026年 10月 19日（月）〜10月 23日（金）
講演者：竹居 正登 氏（横浜国立大学）
題目：エレファントランダムウォークに関する極限定理
談話会と集中講義の概要

2026年 10月 30日 (金) 17:00--18:30
発表者：藪奥 哲史 氏 (福岡大学)
会場：東北大学 理学研究科合同Ａ棟 8階 803室 (合同A棟はキャンパスマップのH-02) 

題目：Eigenvalues and eigenvector-overlaps of the non-Hermitian matrix-valued Brownian motion

概要：We consider the non-Hermitian matrix-valued stochastic process whose entries evolve as independent complex Brownian motions. This process is a natural time-dependent model of Ginibre ensemble in random matrix theory. Because of the non-normality of matrices, its eigenvalue processes should be treated together with their eigenvector-overlap processes. Here, the eigenvector-overlap processes are defined by the products of the inner products of corresponding right and left eigenvectors, and they determine the quadratic variations of eigenvalues. Although right and left eigenvectors are defined only up to scaling, eigenvector-overlaps are invariant under such transformations, and hence they are uniquely determined.

In our previous work [1], we derived SDEs for the eigenvector-overlap processes. However, the joint system of eigenvalues and eigenvector-overlaps is not closed by itself. In this talk, we introduce generalized eigenvector-overlaps processes and present an extended system consisting of eigenvalues and these generalized overlaps.

This is based on the joint work with Syota Esaki (Tokyo University of Science), Makoto Katori (Chuo University)  and Jacek Malecki (Wroclaw University of Science and Technology).

[1] Esaki, S., Katori, M., Yabuoku, S.: Eigenvalues, eigenvector-overlaps, and regularized Fuglede--Kadison determinant of the non-Hermitian matrix-valued Brownian motion. J. Math. Phys. {\bf 67}, 063302 (2026).

2026年 11月 20日 (金) 17:00--18:30
発表者：江崎 翔太 氏 (東京理科大学)
会場：東北大学 理学研究科合同Ａ棟 8階 803室 

2026年 11月 27日 (金) 17:00--18:30
発表者：角田 謙吉 氏 (九州大学)
会場：東北大学 理学研究科合同Ａ棟 8階 803室 

2026年 12月 17日 (木) 17:00--18:30 
発表者：坂井 哲 氏 (北海道大学)
会場：東北大学 理学研究科合同Ａ棟 12階 1201室