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math.PR2023
Normal approximation for statistics of randomly weighted complexes
Shu Kanazawa, Khanh Duy Trinh, D. Yogeshwaran
We prove normal approximation bounds for statistics of randomly weighted (simplicial) complexes. In particular, we consider the complete -dimensional complex on vertices wit…
math.PR2023
Central limit theorem for linear eigenvalue statistics of the adjacency matrices of random simplicial complexes
Shu Kanazawa, Khanh Duy Trinh
We study the adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erdős-Rényi graph model. Recently, Knowles and Rosenthal pro…
math.PR2023
Beta Jacobi ensembles and associated Jacobi polynomials, II
Fumihiko Nakano, Hoang Dung Trinh, Khanh Duy Trinh
In a high temperature regime, it was shown in Trinh--Trinh (\emph{J.\ Stat.\ Phys.}\ \textbf{185}(1), Paper No.\ 4, 15 (2021)) that the empirical distribution of beta Jacobi ensemb…