Random Matrices with External Source and KP τ Functions
نویسنده
چکیده
Due to the unitary-invariance, we assume A = diag(a1, . . . , an), ai ∈ R without loss of generality. We consider Zn(A) as a function of eigenvalues of A, and find a KP τ function property of it. Zn(A) arises in the random matrix model with external source [7], [8], [23], [24]. Let A ∈ H be an n × n Hermitian matrix, and V (x) be a function defined on R, such that e (x) decays sufficiently fast. We consider the ensemble of n×n Hermitian matrices with the probability density function
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