Limit Correlation Functions for Fixed Trace Random Matrix Ensembles
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چکیده
LetHN be the set of all N×N (complex) Hermitian matrices, and let trA = ∑N i=1 aii denotes the trace of a square matrix A = (aij) N i,j=1. HN is a real Hilbert space of dimension N with respect to the symmetric bilinear form (A,B) 7→ trAB. Let lN denotes the unique Lebesgue measure on HN which satisfies the relation lN(Q) = 1 for every cube Q ⊂ HN with edges of length 1. A Gaussian probability measure on HN invariant with respect to all orthogonal linear transformations of HN is uniquely defined up to a scaling transformation. Such measures form a one-parameter family (μN)s>0, where the measure μ s N is specified by its density
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تاریخ انتشار 2006