Madan Lal Mehta 2002 J. Phys. A: Math. Gen. 35 517 doi:10.1088/0305-4470/35/3/305
Madan Lal Mehta1
Show affiliationsErcolani and McLaughlin have recently shown that the zeros of the bi-orthogonal polynomials with the weight w(x, y) = exp[−(V1(x) + V2(y) + 2cxy)/2], relevant to a model of two coupled Hermitian matrices, are real and simple. We show that their argument applies to the more general case of the weight (w1 * w2 * ... * wj)(x, y), a convolution of several weights of the same form. This general case is relevant to a model of several Hermitian matrices coupled in a chain. Their argument also works for more general weights such as W(x, y) = e−x−y/(x + y), 0 ≤ x, y < ∞, and for a convolution of several such weights.
15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
Issue 3 (25 January 2002)
Received 3 September 2001, in final form 1 November 2001
Published 11 January 2002
Madan Lal Mehta 2002 J. Phys. A: Math. Gen. 35 517
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