Equilibrium measures in the presence of certain rational external fields

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:431

Article

Orive, R.¹  Sanchez-Lara, J.² 

[1] Univ La Laguna, Dept Anal Matemat, Canary Isl, Spain

[2] Univ Granada, Dept Matemat Aplicada, E-18071 Granada, Spain

关键词: Equilibrium measures;    External fields;    Phase transitions;   

DOI  :  10.1016/j.jmaa.2015.06.022

来源: Elsevier

【 摘 要 】

Equilibrium measures in the real axis in the presence of rational external fields are considered. These external fields are called rational since their derivatives are rational functions. We analyze the evolution of the equilibrium measure, and its support, when the size of the measure, t, or other parameters in the external field vary. Our analysis is illustrated by studying with detail the case of a generalized Gauss-Penner model, which, in addition to its mathematical relevance, has important physical applications (in the framework of random matrix models). This paper is a natural continuation of [18], where equilibrium measures in the presence of polynomial external fields are thoroughly studied. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free