Limit theorems for linear spectrum statistics of orthogonal polynomial ensembles and their applications in random matrix theory
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Physics"
DOI: 10.1063/1.5006507
Abstract: In this paper, we consider the asymptotic behavior of Xfn(n)≔∑i=1nfn(xi), where xi,i=1,…,n form orthogonal polynomial ensembles and fn is a real-valued, bounded measurable function. Under the condition that VarXfn(n)→∞, the Berry-Esseen (BE) bound and Cramer… read more here.
Keywords: linear spectrum; limit theorems; orthogonal polynomial; spectrum statistics ... See more keywords
Moments of discrete orthogonal polynomial ensembles
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DOI: 10.1214/20-ejp472
Abstract: We obtain factorial moment identities for the Charlier, Meixner and Krawtchouk orthogonal polynomial ensembles. Building on earlier results by Ledoux [Elect. J. Probab. 10, (2005)], we find hypergeometric representations for the factorial moments when the… read more here.
Keywords: discrete orthogonal; moments discrete; factorial moments; polynomial ensembles ... See more keywords