Regularity of a vector potential problem and its spectral curve

2008/04/30 by F. Balogh, M. Bertola, Balogh, F. +1
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.0804.4700

v2: Minor corrections suggested by referees

arxiv created 2008/10/27 · arxiv updated 2009/12/01

Abstract

In this note we study a minimization problem for a vector of measures subject to a prescribed interaction matrix in the presence of external potentials. The conductors are allowed to have zero distance from each other but the external potentials satisfy a growth condition near the common points. We then specialize the setting to a specific problem on the real line which arises in the study of certain biorthogonal polynomials (studied elsewhere) and we prove that the equilibrium measures solve a pseudo-algebraic curve under the assumption that the potentials are real analytic. In particular the supports of the equilibrium measures are shown to consist of a finite union of compact intervals.

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