Riemann-Hilbert approach to a generalised sine kernel

2019/05/13 by Roozbeh Gharakhloo, Gharakhloo, R., A. R. Its +3
Computer Science · Mathematics · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Matrix Theory and Algorithms #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1905.04907

openalex publication_date 2019/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive the large distance asymptotics of the Fredholm determinant of the so-called generalised sine kernel at the critical point. This kernel corresponds to a generalisation of the pure sine kernel arising in the theory of random matrices and has potential applications to the analysis of the large-distance asymptotic behaviour of the so-called emptiness formation probability for various quantum integrable models away from their free fermion point.

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