Grava, TamaraTian, Fei-Ran20052011-09-0720052011-09-072005Commun. Math. Sci. 4 (2006) 551-573https://openscience.sissa.it/handle/1963/1789We 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).291341 bytesapplication/pdfen-USPreprint