Random matrices with equispaced external source
(2014) Communications in Mathematical Physics — Vol. 328, n° 3, p. 1023-1077 (2014)
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- Abstract
- We study Hermitian random matrix models with an external source matrix which has equispaced eigenvalues, and with an external eld such that the limiting mean density of eigenvalues is supported on a single interval as the dimension tends to innity. We obtain strong asymptotics for the multiple orthogonal polynomials associated to these models, and as a consequence for the average characteristic polynomials. One feature of the multiple orthogonal polynomials analyzed in this paper is that the number of orthogonality weights of the polynomials grows with the degree. Nevertheless we are able to characterize them in terms of a pair of 2 1 vector-valued Riemann-Hilbert problems, and to perform an asymptotic analysis of the Riemann-Hilbert problems.
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Claeys, T., & Wang, D. (2014). Random matrices with equispaced external source. Communications in Mathematical Physics, 328(3), 1023-1077. https://doi.org/10.1007/s00220-014-1988-y (Original work published 2014)