On the integrable structure of deformed sine kernel determinants

2023/09/07 by Claeys, Tom, Tarricone, Sofia · 2 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2309.03803

Abstract

We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function w. For a specific choice of w, this kernel describes bulk statistics of finite temperature free fermions. We establish a connection between these determinants and a system of integro-differential equations generalizing the fifth Painlevé equation, and we show that they allow us to solve an integrable PDE explicitly for a large class of initial data.

Cited by

• On Fredholm Pfaffians and Riemann-Hilbert problems
• Deformations of OP ensembles in a bulk critical scaling

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