Regularity of a vector potential problem and its spectral curve

Details Regularity of a vector potential problem and its spectral curve Regularity of a vector potential problem and its spectral curve

2008-04-30

arxiv.org/abs/0804.4700v2

Physics

Mathematical Physics

v2: Minor corrections suggested by referees

Scientific paper

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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