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

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 analyz...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2015-08, Vol.284, p.10-25
Main Authors: Álvarez, Gabriel, Martínez Alonso, Luis, Medina, Elena
Format: Article
Language:English
Subjects:
Asymptotic properties
Density
Mathematical analysis
Mathematical models
Orthogonal polynomials
Phase transformations
Phase transitions
Polynomials
Solid phases
Standard cubic model
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2014.11.054