Browsing by Author "Tian, Fei-Ran"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Large Parameter Behavior of Equilibrium Measures
    (2005) Grava, Tamara; Tian, Fei-Ran; Mathematics; Mathematical Physics
    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).