Global and Local Scaling Limits for Linear Eigenvalue Statistics of Jacobi $\beta$-Ensembles
Mathematical Physics
2023-08-21 v2 math.MP
Abstract
We study the moment-generating functions (MGF) for linear eigenvalue statistics of Jacobi unitary, symplectic and orthogonal ensembles. By expressing the MGF as Fredholm determinants of kernels of finite rank, we show that the mean and variance of the suitably scaled linear statistics in these Jacobi ensembles are related to the sine kernel in the bulk of the spectrum, whereas they are related to the Bessel kernel at the (hard) edge of the spectrum. The relation between the Jacobi symplectic/orthogonal ensemble (JSE/JOE) and the Jacobi unitary ensemble (JUE) is also established.
Keywords
Cite
@article{arxiv.2111.05661,
title = {Global and Local Scaling Limits for Linear Eigenvalue Statistics of Jacobi $\beta$-Ensembles},
author = {Chao Min and Yang Chen},
journal= {arXiv preprint arXiv:2111.05661},
year = {2023}
}
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27 pages