Painlevé I double scaling limit in the cubic random matrix model

DOI10.1142/S2010326316500040zbMath1339.30013arXiv1310.3768MaRDI QIDQ2809329

Alfredo Deaño, Pavel M. Bleher

Publication date: 27 May 2016

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.3768

zbMATH Keywords

random matricesRiemann-Hilbert problemsPainlevé I equationasymptotic representation in the complex domain

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Planar graphs; geometric and topological aspects of graph theory (05C10) Riemann-Hilbert problems in context of PDEs (35Q15) Painlevé-type functions (33E17) Asymptotic representations in the complex plane (30E15)

Related Items (12)

Investigation of the two-cut phase region in the complex cubic ensemble of random matrices ⋮ Large \(z\) asymptotics for special function solutions of Painlevé II in the complex plane ⋮ Relating random matrix map enumeration to a universal symbol calculus for recurrence operators in terms of Bessel–Appell polynomials ⋮ On the Riemann–Hilbert approach to asymptotics of tronquée solutions of Painlevé I ⋮ Universality for multiplicative statistics of Hermitian random matrices and the integro-differential Painlevé II equation ⋮ Phase diagram and topological expansion in the complex quartic random matrix model ⋮ The Mother Body Phase Transition in the Normal Matrix Model ⋮ Do orthogonal polynomials dream of symmetric curves? ⋮ Topological expansion in the complex cubic log-gas model: one-cut case ⋮ Spectral curves, variational problems and the Hermitian matrix model with external source ⋮ Multiple scale asymptotics of map enumeration ⋮ Generalised Airy polynomials

Uses Software

• DLMF

Cites Work

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