The entries of circular orthogonal ensembles
نویسندگان
چکیده
منابع مشابه
The Entries of Circular Orthogonal Ensembles
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 sequ...
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Let μ be a measure with support on the unit circle and n ≥ 1, β > 0. The associated circular β ensemble involves a probability distribution of the form P β (μ; t1, t2, ..., tn) = C |V (t1, t2, ..., tn)| β dμ (t1) ...dμ (tn) , where C is a normalization constant, and V (t1, t2, ..., tn) = ∏ 1≤i<j≤n (tj − ti) . We explicitly evaluate the m−point correlation functions when μ is replaced by a discr...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2009
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.3152217