A Phase Transition for Nonintersecting Brownian Motions, and the Painleve II Equation

DOI10.1093/imrn/rnp069zbMath1182.60023arXiv0809.1000OpenAlexW2963594095MaRDI QIDQ3182292

Steven Delvaux, Arno B. J. Kuijlaars

Publication date: 8 October 2009

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.1000

zbMATH Keywords

Brownian motionRiemann-Hilbert problemlimiting distributionPainlevé II equation

Mathematics Subject Classification ID

Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Phase transitions (general) in equilibrium statistical mechanics (82B26) Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics (82B41) Ordinary differential equations in the complex domain (34Mxx)

Related Items (11)

Location of poles for the Hastings-McLeod solution to the second Painlevé equation ⋮ A critical phenomenon in the two-matrix model in the quartic/quadratic case ⋮ Non-intersecting squared Bessel paths with one positive starting and ending point ⋮ Nonintersecting random walks in the neighborhood of a symmetric tacnode ⋮ A graph-based equilibrium problem for the limiting distribution of nonintersecting Brownian motions at low temperature ⋮ Non-intersecting squared Bessel paths at a hard-edge tacnode ⋮ Non-intersecting Brownian motions leaving from and going to several points ⋮ Non-colliding Brownian motions and the extended tacnode process ⋮ Airy processes with wanderers and new universality classes ⋮ Large complex correlated Wishart matrices: fluctuations and asymptotic independence at the edges ⋮ Random matrix model with external source and a constrained vector equilibrium problem

This page was built for publication: A Phase Transition for Nonintersecting Brownian Motions, and the Painleve II Equation