PDE's for the Dyson, Airy and Sine processes.

DOI10.5802/aif.2143zbMath1085.60028OpenAlexW2502984025MaRDI QIDQ2574189

Mark Adler

Publication date: 18 November 2005

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2005__55_6_1835_0

zbMATH Keywords

Dyson's Brownian motionAiry processcoupled Gaussian Hermitian matrices

Mathematics Subject Classification ID

Random fields (60G60) Stationary stochastic processes (60G10) KdV equations (Korteweg-de Vries equations) (35Q53) Local time and additive functionals (60J55)

Cites Work

• On asymptotics for the Airy process
• Differential equations for Dyson processes
• The spectrum of coupled random matrices
• Level-spacing distributions and the Airy kernel
• Scale invariance of the PNG droplet and the Airy process
• Correlations for the orthogonal-unitary and symplectic-unitary transitions at the hard and soft edges
• A system of differential equations for the Airy process
• PDEs for the joint distributions of the Dyson, Airy and Sine processes
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix