Fluctuations of the eigenvalue number in the fixed interval for $\beta$-models with $\beta=1,2,4$

Autor:	Shcherbina, Mariya
Rok vydání:	2015
Předmět:	Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	We study the fluctuation of the eigenvalue number of any fixed interval $\Delta=[a,b]$ inside the spectrum for $\beta$- ensembles of random matrices in the case $\beta=1,2,4$. We assume that the potential $V$ is polynomial and consider the cases of any multi-cut support of the equilibrium measure. It is shown that fluctuations become gaussian in the limit $n\to\infty$, if they are normalized by $\pi^{-2}\log n$. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1504.05758 Zobrazit plný text záznamu View this record from Arxiv