00940nas a2200109 4500008004300000245005300043210005300096520060900149100001800758700001800776856003600794 2006 en_Ud 00aLarge Parameter Behavior of Equilibrium Measures0 aLarge Parameter Behavior of Equilibrium Measures3 aWe 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).1 aGrava, Tamara1 aTian, Fei-Ran uhttp://hdl.handle.net/1963/1789