Monday, November 26, 2012

1211.5369 (M. Bertola et al.)

Cauchy-Laguerre two-matrix model and the Meijer-G random point field    [PDF]

M. Bertola, M. Gekhtman, J. Szmigielski
We apply the general theory of Cauchy biorthogonal polynomials developed in previous works to the case associated with Laguerre measures. In particular, we obtain explicit formulae in terms of Meijer-G functions for all key objects relevant to the study of the corresponding biorthogonal polynomials and the Cauchy two-matrix model associated with them. The central theorem proved for such Cauchy two-matrix model is that a scaling limit of the correlation functions for eigenvalues near the origin exists and is given by certain new random point field, the "Meijer-G random field". We conjecture that this random point field leads to a novel universality class of random fields parametrized by exponents of Laguerre weights.
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