An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model

Details An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model

2011-01-14

arxiv.org/abs/1101.2727v1

Nucl.Phys.B848:398-429,2011

Physics

Mathematical Physics

Scientific paper

10.1016/j.nuclphysb.2011.02.019

We present a method to compute the genus expansion of the free energy of Hermitian matrix models from the large N expansion of the recurrence coefficients of the associated family of orthogonal polynomials. The method is based on the Bleher-Its deformation of the model, on its associated integral representation of the free energy, and on a method for solving the string equation which uses the resolvent of the Lax operator of the underlying Toda hierarchy. As a byproduct we obtain an efficient algorithm to compute generating functions for the enumeration of labeled k-maps which does not require the explicit expressions of the coefficients of the topological expansion. Finally we discuss the regularization of singular one-cut models within this approach.

Affiliated with

Also associated with

No associations

Rating

An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An efficient method for computing genus expansions and counting numbers in the Hermitian matrix model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-78537