Large Parameter Behavior of Equilibrium Measures
Grava, Tamara ; Tian, Fei-Ran
arXiv, 0506040 / Harvested from arXiv
Text on arXiv
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).
Publié le : 2005-06-15
Classification:  Mathematical Physics,  Mathematics - Classical Analysis and ODEs,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0506040,
     author = {Grava, Tamara and Tian, Fei-Ran},
     title = {Large Parameter Behavior of Equilibrium Measures},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506040}
}

Grava, Tamara; Tian, Fei-Ran. Large Parameter Behavior of Equilibrium Measures. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506040/