Asymptotics via Steepest Descent for an Operator Riemann-Hilbert Problem
Functional Analysis
2007-05-23 v1
Abstract
In this paper, we take the first step towards an extension of the nonlinear steepest descent method of Deift, Its and Zhou to the case of operator Riemann-Hilbert problems. In particular, we provide long range asymptotics for a Fredholm determinant arising in the computation of the probability of finding a string of n adjacent parallel spins up in the antiferromagnetic ground state of the spin 1/2 XXX Heisenberg Chain. Such a determinant can be expressed in terms of the solution of an operator Riemann-Hilbert factorization problem.
Cite
@article{arxiv.math/9907053,
title = {Asymptotics via Steepest Descent for an Operator Riemann-Hilbert Problem},
author = {Spyridon Kamvissis},
journal= {arXiv preprint arXiv:math/9907053},
year = {2007}
}