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Phase structure and asymptotic zero densities of orthogonal polynomials in the cubic model

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Álvarez Galindo, Gabriel and Martínez Alonso, Luis and Medina Reus, Elena (2015) Phase structure and asymptotic zero densities of orthogonal polynomials in the cubic model. Journal of computational and applied mathematics, 284 . pp. 10-25. ISSN 0377-0427

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Official URL: http://dx.doi.org/10.1016/j.cam.2014.11.054


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Abstract

We apply the method we have described in a previous paper (2013) to determine the phase structure of asymptotic zero densities of the standard cubic model of non-Hermitian orthogonal polynomials. We provide a complete description of the two phases: the one cut phase and the two cut phase, and analyze the phase transition processes of the types: splitting of a cut, birth and death of a cut. (C) 2014 Elsevier B.V. All rights reserved.


Item Type:Article
Additional Information:

© Elsevier Science Bv.
We thank Prof. A. Martínez Finkelshtein for useful conversations and for calling our attention to the work [20]. The financial support of the Ministerio de Ciencia e Innovación under project FIS2011-22566 is gratefully acknowledged.

Uncontrolled Keywords:Riemann-hilbert approach; Valued weight function; Matrix models; Exponential weights; Respect; Universality
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30419
Deposited On:28 May 2015 08:30
Last Modified:10 Dec 2018 15:09

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