Equilibrium measures in the presence of weak rational external fields

Ramon Orive; Joaquin F. Sanchez Lara

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arXiv · 1605.01909

Equilibrium measures in the presence of weak rational external fields

Ramon Orive·Joaquin F. Sanchez Lara

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Abstract

In this paper equilibrium measures in the presence of external fields created by fixed charges are analyzed. These external fields are a particular case of the so-called rational external fields (in the sense that their derivatives are rational functions). Along with some general results, a thorough analysis of the particular case of two fixed negative charges (``attractors') is presented. As for the main tools used, this paper is a natural continuation of \cite{MOR2015}, where polynomial external fields were thoroughly studied, and \cite{OrSL2015}, where rational external fields with a polynomial part were considered. However, the absence of the polynomial part in the external fields analyzed in the current paper adds a considerable difficulty to solve the problem and justifies its separated treatment; moreover, it is noteworthy to point out the simplicity and beauty of the results obtained.

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Ramon Orive, Joaquin F. Sanchez Lara. 2016-05-06. Equilibrium measures in the presence of weak rational external fields. https://arxiv.org/abs/1605.01909

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