Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Trinh, Khanh Duy"'
We prove normal approximation bounds for statistics of randomly weighted (simplicial) complexes. In particular, we consider the complete $d$-dimensional complex on $n$ vertices with $d$-simplices equipped with i.i.d. weights. Our normal approximation
Externí odkaz:
http://arxiv.org/abs/2312.07771
Autor:
Kanazawa, Shu, Trinh, Khanh Duy
We study the adjacency matrix of the Linial-Meshulam complex model, which is a higher-dimensional generalization of the Erd\H{o}s-R\'enyi graph model. Recently, Knowles and Rosenthal proved that the empirical spectral distribution of the adjacency ma
Externí odkaz:
http://arxiv.org/abs/2308.11540
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 ensembles converges to a limiting probability measure which is related to Mo
Externí odkaz:
http://arxiv.org/abs/2304.10734
Publikováno v:
Random Matrices: Theory and Applications 2023
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 Laguerre ensembles) converges to a probability measure of associated Herm
Externí odkaz:
http://arxiv.org/abs/2103.09980
Autor:
Trinh, Hoang Dung, Trinh, Khanh Duy
Publikováno v:
J Stat Phys 185, 4 (2021)
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 deals with beta Jacobi ensembles, the type with the Jacobi weight. Maki
Externí odkaz:
http://arxiv.org/abs/2005.01100
Autor:
Trinh, Hoang Dung, Trinh, Khanh Duy
Publikováno v:
Stochastic Processes and their Applications 2021
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 paper, we study the limiting behavior of their empirical measure proce
Externí odkaz:
http://arxiv.org/abs/2004.14613
Autor:
Can, Van Hao, Trinh, Khanh Duy
The paper deals with a random connection model, a random graph whose vertices are given by a homogeneous Poisson point process on $\mathbb{R}^d$, and edges are independently drawn with probability depending on the locations of the two end points. We
Externí odkaz:
http://arxiv.org/abs/2004.06313
Autor:
Nakano, Fumihiko, Trinh, Khanh Duy
Publikováno v:
Journal of Statistical Physics 2020
This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $\beta N \to const \in (0, \infty)$, with $N$ the system size and $\beta$ the inverse temperature. In this regime, the convergence to the equil
Externí odkaz:
http://arxiv.org/abs/1910.00766
Autor:
Trinh, Hoang Dung, Trinh, Khanh Duy
Beta Laguerre ensembles which are generalizations of Wishart ensembles and Laguerre ensembles can be realized as eigenvalues of certain random tridiagonal matrices. Analogous to the Wishart ($\beta=1$) case and the Laguerre ($\beta = 2$) case, for fi
Externí odkaz:
http://arxiv.org/abs/1907.12267
Autor:
Trinh, Khanh Duy
The paper studies the relation between critical simplices and persistence diagrams of the \v{C}ech filtration. We show that adding a critical $k$-simplex into the filtration corresponds either to a point in the $k$th persistence diagram or a point in
Externí odkaz:
http://arxiv.org/abs/1902.08063