Asymptotics of a Fredholm determinant corresponding to the first bulk critical universality class in random matrix models

DOI10.1007/s00220-014-1950-zzbMath1290.15004OpenAlexW2125223937MaRDI QIDQ2452198

Thomas Bothner, Alexander R. Its

Publication date: 30 May 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1805/3655

zbMATH Keywords

second Painlevé equationFredholm determinanteigenvalue densityrandom Hermitian matrixunitary ensembleHastings-McLeod solutionRiemann-Hilbert methodintegrable Fredholm operator

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) (Semi-) Fredholm operators; index theories (47A53) Random matrices (algebraic aspects) (15B52)

Related Items (7)

A Poincaré determinant on the torus ⋮ Tracy-Widom distributions in critical unitary random matrix ensembles and the coupled Painlevé II system ⋮ Gap Probability at the Hard Edge for Random Matrix Ensembles with Pole Singularities in the Potential ⋮ Approximation property and nuclearity on mixed‐normL^p, modulation and Wiener amalgam spaces ⋮ Determinants and Plemelj-Smithies formulas ⋮ Fredholm determinant representation of the homogeneous Painlevé II τ-function ⋮ Asymptotics of a cubic sine kernel determinant

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