Large Parameter Behavior of Equilibrium Measures

Details Large Parameter Behavior of Equilibrium Measures Large Parameter Behavior of Equilibrium Measures

2005-06-15

arxiv.org/abs/math-ph/0506040v1

Physics

Mathematical Physics

32 pages

Scientific paper

We study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium measure is shown to be supported on a single interval as |t| is sufficiently large. When p(x) is of an even degree, the equilibrium measure is supported on two disjoint intervals as t is negatively large; it is supported on a single interval for convex p(x) as t is positively large and is likely to be supported on multiple disjoint intervals for non-convex p(x).

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