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

• Gabriel Álvarez ^[1] ; Luis Martínez Alonso ^[1] ; Elena Medina ^[2]
  1. [1] Universidad Complutense de Madrid

     Universidad Complutense de Madrid

     Madrid, España

     
  2. [2] Universidad de Cádiz

     Universidad de Cádiz

     Cádiz, España

     
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 284, Nº 1 (15 August 2015), 2015, págs. 10-25
• Idioma: inglés
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• Resumen

  • 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.