The entries of circular orthogonal ensembles | Zendy

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The entries of circular orthogonal ensembles

Author(s) -

Tiefeng Jiang

Publication year - 2009

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.3152217

Subject(s) - combinatorics , independent and identically distributed random variables , circular law , mathematics , distribution (mathematics) , sequence (biology) , random matrix , random variable , physics , matrix (chemical analysis) , mathematical analysis , quantum mechanics , statistics , eigenvalues and eigenvectors , sum of normally distributed random variables , chemistry , biochemistry , chromatography

Let V = (vij)n£n be a circular orthogonal ensemble. In this paper, for 1 • m • o( p n=logn), we give a bound for the tail probability of max1•i;jm jvij ¡ (1=n)y0iyjj; where Y = (y1;¢¢¢ ;yn) is a certain n£n matrix whose entries are independent and identically distributed ran- dom variables with the standard complex normal distribution CN(0;1): In particular, this implies that, for a sequence of such matrices fVn = (v (n)

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