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6 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…
Eigenvalue statistics for random polymer models: Localization and delocalization
Peter D. Hislop, Fumihiko Nakano
We study the local eigenvalue statistics (LES) associated with one-dimensional lattice models of random polymers. We consider models constructed from two polymers. Each polymer is…
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…
Non-isomorphic Cayley Graphs with Same Random Walk Distributions
Masao Ishikawa, Fumihiko Nakano, Taizo Sadahiro
We construct an infinite family of triples (G,S1, S2) each consisting of a group G and a pair (S1, S2) of distinct subsets of G with the following properties. i The two Cayley grap…
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…