Non-intersecting Brownian bridges and the Laguerre orthogonal ensemble

DOI10.1214/16-AIHP781zbMath1382.60122arXiv1505.01708OpenAlexW854188118MaRDI QIDQ1700403

Daniel Remenik, Gia Bao Nguyen

Publication date: 5 March 2018

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.01708

zbMATH Keywords

random matricesKPZ universality classnon-intersecting Brownian motions\(\mathrm{Airy}_{2}\) process

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35)

Related Items (10)

Brownian bridges for late time asymptotics of KPZ fluctuations in finite volume ⋮ Point-to-line last passage percolation and the invariant measure of a system of reflecting Brownian motions ⋮ Tracy-Widom distributions for the Gaussian orthogonal and symplectic ensembles revisited: a skew-orthogonal polynomials approach ⋮ How flat is flat in random interface growth? ⋮ Non-crossing Brownian paths and Dyson Brownian motion under a moving boundary ⋮ Lower deviations in \(\beta \)-ensembles and law of iterated logarithm in last passage percolation ⋮ Interacting diffusions on positive definite matrices ⋮ The invariant measure of PushASEP with a wall and point-to-line last passage percolation ⋮ Constrained non-crossing Brownian motions, fermions and the Ferrari–Spohn distribution ⋮ Airy process with wanderers, KPZ fluctuations, and a deformation of the Tracy-Widom GOE distribution

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Exact formulas for random growth with half-flat initial data
• Local behavior and hitting probabilities of the \(\text{Airy}_1\) process
• Non-colliding Brownian bridges and the asymmetric tacnode process
• Nonintersecting Brownian motions on the half-line and discrete Gaussian orthogonal polynomials
• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Characteristic vectors of bordered matrices with infinite dimensions
• Coincidence probabilities
• Differential equations for Dyson processes
• Renormalization fixed point of the KPZ universality class
• The one-dimensional KPZ equation and its universality class
• Airy processes with wanderers and new universality classes
• The \(\text{Airy}_{1}\) process is not the limit of the largest eigenvalue in GOE matrix diffusion
• Binomial determinants, paths, and hook length formulae
• Walks, walls, wetting, and melting
• Level-spacing distributions and the Airy kernel
• Scale invariance of the PNG droplet and the Airy process
• Discrete polynuclear growth and determinantal processes
• Correlations for superpositions and decimations of Laguerre and Jacobi orthogonal matrix ensembles with a parameter
• On the distribution of the largest eigenvalue in principal components analysis
• On orthogonal and symplectic matrix ensembles
• Continuum statistics of the Airy\(_{2}\) process
• Endpoint distribution of directed polymers in \(1 + 1\) dimensions
• Non-colliding Brownian motions and the extended tacnode process
• Shape fluctuations and random matrices
• Multiplicative functionals on ensembles of non-intersecting paths
• Brownian Gibbs property for Airy line ensembles
• Integrable probability: from representation theory to MacDonald processes
• Random matrix central limit theorems for nonintersecting random walks
• Nonintersecting Brownian excursions
• Fluctuation properties of the TASEP with periodic initial configuration
• Noncolliding Brownian motion and determinantal processes
• PDEs for the joint distributions of the Dyson, Airy and Sine processes
• The propagator of the attractive delta-Bose gas in one dimension
• The height of watermelons with wall
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• THE KARDAR-PARISI-ZHANG EQUATION AND UNIVERSALITY CLASS
• General β-Jacobi Corners Process and the Gaussian Free Field
• Exact Distribution of the Maximal Height of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math>Vicious Walkers
• Critical behavior of nonintersecting Brownian motions at a tacnode
• Airy Processes and Variational Problems
• The Height and Range of Watermelons without Wall
• On the Vector Representations of Induced Matroids

This page was built for publication: Non-intersecting Brownian bridges and the Laguerre orthogonal ensemble