Large Parameter Behavior of Equilibrium Measures
数学物理
2015-10-07 v1 经典分析与常微分方程
math.MP
可精确求解与可积系统
摘要
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).
引用
@article{arxiv.math-ph/0506040,
title = {Large Parameter Behavior of Equilibrium Measures},
author = {Tamara Grava and Fei-Ran Tian},
journal= {arXiv preprint arXiv:math-ph/0506040},
year = {2015}
}
备注
32 pages