Gaëtan Borot, Alice Guionnet
We push further our study of the all-order asymptotic expansion in $\beta$ matrix models with a confining, offcritical potential, in the regime where the support of the equilibrium measure is a reunion of segments. We first address the case where the filling fractions of those segments are fixed, and show the existence of a 1/N expansion to all orders. Then, we study the asymptotic of the sum over filling fractions, in order to obtain the full asymptotic expansion for the initial problem in the multi-cut regime. We describe the application of our results to study the all-order small dispersion asymptotics of solutions of the Toda chain related to the one hermitian matrix model (beta = 2) as well as orthogonal polynomials outside the bulk. Our results would also apply to the all-order asymptotic expansion of skew-orthogonal polynomials (beta = 1 and 4) outside the bulk.
View original:
http://arxiv.org/abs/1303.1045
No comments:
Post a Comment