Central limit theorem for linear eigenvalue statistics of the adjacency matrices of random simplicial complexes
開催期間
16:30 ~ 18:00
場所
講演者
概要
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).