Discrete Derivative Asymptotics of the $\beta$-Hermite Eigenvalues
Probability
2019-01-30 v3
Abstract
We consider the asymptotics of the difference between the empirical measures of the -Hermite tridiagonal matrix and its minor. We prove that this difference has a deterministic limit and Gaussian fluctuations. Through a correspondence between measures and continual Young diagrams, this deterministic limit is identified with the Vershik-Kerov-Logan-Shepp curve. Moreover, the Gaussian fluctuations are identified with a sectional derivative of the Gaussian free field.
Keywords
Cite
@article{arxiv.1809.06804,
title = {Discrete Derivative Asymptotics of the $\beta$-Hermite Eigenvalues},
author = {Gopal Goel and Andrew Ahn},
journal= {arXiv preprint arXiv:1809.06804},
year = {2019}
}
Comments
16 pages, 3 figures