Strong asymptotics for Cauchy biorthogonal polynomials
نویسندگان
چکیده
where U, V are scalar functions defined on R. The model was termed the Cauchy matrix model because of the shape of the coupling term. Similarly to the case of the Hermitean one-matrix models for which the spectral statistics is expressible in terms of appropriate orthogonal polynomials [3], this two-matrix model is solvable with the help of a new family of biorthogonal polynomials named the Cauchy biorthogonal polynomials [4]. The Cauchy biorthogonal polynomials are two sequences of monic polynomials (pj(x))j=0, (qj(y)) ∞ j=0 with deg pj =deg qj = j that satisfy ∫∫
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