Multilevel Dyson Brownian motions via Jack polynomials

DOI10.1007/s00440-014-0596-2zbMath1334.60160arXiv1401.5595OpenAlexW1994668498MaRDI QIDQ892157

Vadim Gorin, Mykhaylo Shkolnikov

Publication date: 18 November 2015

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.5595

zbMATH Keywords

Jack polynomialsmultilevel discrete Markov chainsmultilevel Dyson Brownian motions

Mathematics Subject Classification ID

Random matrices (probabilistic aspects) (60B20) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Symmetric functions and generalizations (05E05) Interacting particle systems in time-dependent statistical mechanics (82C22) Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Diffusion processes (60J60)

Related Items (24)

Large deviations for discrete \(\beta\)-ensembles ⋮ Interacting particle systems at the edge of multilevel Dyson Brownian motions ⋮ Intertwinings of beta-Dyson Brownian motions of different dimensions ⋮ Asymptotics of discrete \(\beta \)-corners processes via two-level discrete loop equations ⋮ Pieri integral formula and asymptotics of Jack unitary characters ⋮ Perturbations of multiple Schramm-Loewner evolution with two non-colliding Dyson Brownian motions ⋮ Infinite dimensional stochastic differential equations for Dyson's model ⋮ Matrix addition and the Dunkl transform at high temperature ⋮ Gaussian asymptotics of discrete \(\beta \)-ensembles ⋮ The bead process for beta ensembles ⋮ General β-Jacobi Corners Process and the Gaussian Free Field ⋮ Consecutive minors for Dyson's Brownian motions ⋮ Eigenvalue processes of symmetric tridiagonal matrix-valued processes associated with Gaussian beta ensemble ⋮ Freezing limits for Calogero–Moser–Sutherland particle models ⋮ A global large deviation principle for discrete \(\beta \)-ensembles ⋮ HALF-SPACE MACDONALD PROCESSES ⋮ Asymptotic formulas for Macdonald polynomials and the boundary of the \((q,t)\)-Gelfand-Tsetlin graph ⋮ Integrable probability: from representation theory to MacDonald processes ⋮ Law of large numbers and central limit theorems through Jack generating functions ⋮ Observables of Macdonald processes ⋮ Correlation functions of the Pfaffian Schur process using Macdonald difference operators ⋮ Eigenvalues for the minors of Wigner matrices ⋮ Intertwinings for general \(\beta\)-Laguerre and \(\beta\)-Jacobi processes ⋮ Noncolliding Macdonald walks with an absorbing wall

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