arXiv subjects

Ioana Dumitriu

Publications and source records attributed to Ioana Dumitriu.

39 records · Page 3Linked to original sources

arXiv2004

Eigenvalues of Hermite and Laguerre ensembles: Large Beta Asymptotics

In this paper we examine the zero and first order eigenvalue fluctuations for the $β$-Hermite and $β$-Laguerre ensembles, using the matrix models we described in \cite{dumitriu02}, in the limit as $β\to \infty$. We find that the fluctuations are described by Gaussians of variance $O(1/β)$, centered at the roots of a corresponding Hermite (Laguerre) polynomial. We also show that the approximation is very good, even for small values of $β$, by plotting exact level densities versus sum of Gaussians approximations.

math-ph↗

arXiv2003

Path counting and random matrix theory

We establish three identities involving Dyck paths and alternating Motzkin paths, whose proofs are based on variants of the same bijection. We interpret these identities in terms of closed random walks on the halfline. We explain how these identities arise from combinatorial interpretations of certain properties of the $β$-Hermite and $β$-Laguerre ensembles of random matrix theory. We conclude by presenting two other identities obtained in the same way, for which finding combinatorial proofs is an open problem.

math.CO↗

arXiv2002

Matrix Models for Beta Ensembles

This paper constructs tridiagonal random matrix models for general ($β>0$) $β$-Hermite (Gaussian) and $β$-Laguerre (Wishart) ensembles. These generalize the well-known Gaussian and Wishart models for $β= 1,2,4$. Furthermore, in the cases of the $β$-Laguerre ensembles, we eliminate the exponent quantization present in the previously known models. We further discuss applications for the new matrix models, and present some open problems.

math-ph↗