Tokyo Probability Seminar

Seminar information archive ~05/02Next seminarFuture seminars 05/03~

Date, time & place Monday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.)
Organizer(s) Makiko Sasada, Shuta Nakajima, Masato Hoshino

2024/12/16

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.
Shu Kanazawa (Kyoto University)
Central limit theorem for linear eigenvalue statistics of the adjacency matrices of random simplicial complexes
[ Abstract ]
We consider the (higher-dimensional) adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erdős-Rényi random graph model. Recently, Knowles and Rosenthal proved that the empirical spectral distribution
of the adjacency matrix is asymptotically given by Wigner's semicircle law in a diluted regime. In this talk, I will present a central limit theorem for the linear eigenvalue statistics for test functions of polynomial growth that is of class C2 on a closed
interval. The proof is based on higher-dimensional combinatorial enumerations and concentration properties of random symmetric matrices. Furthermore, when the test function is a polynomial function, we obtain the explicit formula for the variance of the limiting
Gaussian distribution. This is joint work with Khanh Duy Trinh (Waseda University).