# Large-x analysis of an operator valued Riemann-Hilbert problem

Source: [Large-x analysis of an operator valued Riemann-Hilbert problem](<https://www.sota2.com/research/paper/68fa2dd71e209131ce85d10d>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T16:31:31.017Z

Authors: A.R. Its, K.K. Kozlowski

Published: 2014-11-05T10:25:48.000Z

## Abstract

The purpose of this paper is to push forward the theory of operator-valued Riemann Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method \\textit{\\'{a} la} Deift-Zhou. In the present paper, we demonstrate that the operator-valued Riemann--Hilbert problem arising in the characterisation of so-called $c$-shifted integrable integral operators allows one to extract the large-$x$ asymptotics of the Fredholm determinant associated with such operators.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1411.1216>)

[PDF](<https://arxiv.org/pdf/1411.1216.pdf>)