26 citations · 91 across the 17 of their papers we have counts for
18 papers
Beta Ensembles in the Freezing Regime and Finite Free Convolutions
Fumihiko Nakano, Khanh Duy Trinh, Ziteng Wang
In the freezing regime where the system size N is fixed and the inverse temperature beta tends to infinity, the eigenvalues of Gaussian beta ensembles converge to zeros of the Nth…
The spectral measures of random Jacobi matrices related to beta ensembles at high temperature and Dirichlet processes
Fumihiko Nakano, Hoang Dung Trinh, Khanh Duy Trinh
In a high temperature regime where , the empirical distribution of the eigenvalues of Gaussian beta ensembles, beta Laguerre ensembles and beta Jacobi ensembles converge…
Classical beta ensembles and related eigenvalues processes at high temperature and the Markov--Krein transform
Fumihiko Nakano, Hoang Dung Trinh, Khanh Duy Trinh
The aim of this paper is to identify the limit in a high temperature regime of classical beta ensembles on the real line and related eigenvalue processes by using the Markov--Krein…
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…
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…
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…
Limit theorems for moment processes of beta Dyson's Brownian motions and beta Laguerre processes
Fumihiko Nakano, Hoang Dung Trinh, Khanh Duy Trinh
In the regime where the parameter beta is proportional to the reciprocal of the system size, it is known that the empirical distribution of Gaussian beta ensembles (resp.\ beta Lag…
Beta Jacobi ensembles and associated Jacobi polynomials
Hoang Dung Trinh, Khanh Duy Trinh
Beta ensembles on the real line with three classical weights (Gaussian, Laguerre and Jacobi) are now realized as the eigenvalues of certain tridiagonal random matrices. The paper d…
Beta Laguerre processes in a high temperature regime
Hoang Dung Trinh, Khanh Duy Trinh
Beta Laguerre processes which are generalizations of the eigenvalue process of Wishart/Laguerre processes can be defined as the square of radial Dunkl processes of type B. In this…
Random connection models in the thermodynamic regime: central limit theorems for add-one cost stabilizing functionals
Van Hao Can, Khanh Duy Trinh
The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on , and edges are independently drawn…
Poisson statistics for beta ensembles on the real line at high temperature
Fumihiko Nakano, Khanh Duy Trinh
This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where , with the system size and the inve…
Beta Laguerre ensembles in global regime
Hoang Dung Trinh, Khanh Duy Trinh
Beta Laguerre ensembles which are generalizations of Wishart ensembles and Laguerre ensembles can be realized as eigenvalues of certain random tridiagonal matrices. Analogous to th…
On persistent homology of random Čech complexes
Khanh Duy Trinh
The paper studies the relation between critical simplices and persistence diagrams of the Čech filtration. We show that adding a critical -simplex into the filtration correspond…
Strong law of large numbers for Betti numbers in the thermodynamic regime
Akshay Goel, Khanh Duy Trinh, Kenkichi Tsunoda
We establish the strong law of large numbers for Betti numbers of random Čech complexes built on -valued binomial point processes and related Poisson point processes i…
On central limit theorems in stochastic geometry
Khanh Duy Trinh
We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers…
Global spectrum fluctuations for Gaussian beta ensembles: a martingale approach
Khanh Duy Trinh
The paper describes the global limiting behavior of Gaussian beta ensembles where the parameter is allowed to vary with the matrix size . In particular, we show that as $n \…
Limit theorems for persistence diagrams
Trinh Khanh Duy, Yasuaki Hiraoka, Tomoyuki Shirai
The persistent homology of a stationary point process on is studied in this paper. As a generalization of continuum percolation theory, we study higher dimensional topo…
Gaussian beta ensembles at high temperature: eigenvalue fluctuations and bulk statistics
Trinh Khanh Duy, Fumihiko Nakano
We study the limiting behavior of Gaussian beta ensembles in the regime where as . The results are (1) Gaussian fluctuations for linear statistics of the…