Asymptotics of the Hard Edge Pearcey Determinant

Abstract

.We study the Fredholm determinant of an integral operator associated to the hard edge Pearcey kernel. This determinant appears in a variety of random matrix and nonintersecting paths models. By relating the logarithmic derivatives of the Fredholm determinant to a \(3 \times 3\) Riemann–Hilbert problem, we obtain asymptotics of the determinant, which is also known as the large gap asymptotics for the corresponding point process.Keywordsasymptotic analysisFredholm determinantrandom matrix theoryRiemann–Hilbert problemsMSC codes60B2030E2547N30

Locations

• arXiv (Cornell University) - View - PDF
• SIAM Journal on Mathematical Analysis - View