The entries of circular orthogonal ensembles

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

Let V= (vij)n×n be a circular orthogonal ensemble. In this paper, for 1≤ m ≤ o (n/log n), we give a bound for the tail probability of max1≤ i,j ≤ m vij - (1/n) y′iyj , where Y= (y1, yn) is a certain n×n matrix whose entries are independent and identically distributed random variables with the standard complex normal distribution ℂN (0,1). In particular, this implies that, for a sequence of such matrices {Vn = (vij(n))n×n, n ≥ 1}, as n→∞, n vij (n) converges in distribution to ℂN (0,1) for any i ≥ 1,j ≥ 1 with i ≤ j and n vii(n) converges in distribution to 2 · ℂN (0,1) for any i ≥ 1.

Original languageEnglish (US)
Article number063302
JournalJournal of Mathematical Physics
Volume50
Issue number6
DOIs
StatePublished - 2009

Fingerprint Dive into the research topics of 'The entries of circular orthogonal ensembles'. Together they form a unique fingerprint.

  • Cite this