Infinite dimensional stochastic differential equations for Dyson's model

DOI10.1007/s00440-015-0672-2zbMath1354.60064arXiv1405.6692OpenAlexW3100051027MaRDI QIDQ343791

Li-Cheng Tsai

Publication date: 29 November 2016

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

Full work available at URL: https://arxiv.org/abs/1405.6692

zbMATH Keywords

correlation functionpathwise uniquenessDyson's Brownian motionDyson's modelinfinite-dimensional stochastic differential equationsstrong existence

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting particle systems in time-dependent statistical mechanics (82C22) Brownian motion (60J65) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Diffusion processes (60J60)

Related Items (19)

Dynamical universality for random matrices ⋮ Large deviations in the quantum quasi-1D jellium ⋮ Two-Sided Infinite Systems of Competing Brownian Particles ⋮ Hua-Pickrell diffusions and Feller processes on the boundary of the graph of spectra ⋮ Ergodicity of unlabeled dynamics of Dyson’s model in infinite dimensions ⋮ Stochastic analysis of infinite particle systems—A new development in classical stochastic analysis and dynamical universality of random matrices ⋮ Strong Markov property of determinantal processes with extended kernels ⋮ Exact solution of interacting particle systems related to random matrices ⋮ On the ergodicity of interacting particle systems under number rigidity ⋮ Stochastic differential equations with local interactions ⋮ Conformal welding problem, flow line problem, and multiple Schramm–Loewner evolution ⋮ Dynamical bulk scaling limit of Gaussian unitary ensembles and stochastic differential equation gaps ⋮ Uniqueness of Dirichlet forms related to infinite systems of interacting Brownian motions ⋮ The logarithmic derivative for point processes with equivalent Palm measures ⋮ Infinite-dimensional stochastic differential equations and tail \(\sigma\)-fields II: the IFC condition ⋮ Markov dynamics on the dual object to the infinite-dimensional unitary group ⋮ Infinite-dimensional stochastic differential equations and tail \(\sigma\)-fields ⋮ Dyson's model in infinite dimensions is irreducible ⋮ Stochastic geometry and dynamics of infinitely many particle systems—random matrices and interacting Brownian motions in infinite dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• KPZ line ensemble
• Interacting particle systems at the edge of multilevel Dyson Brownian motions
• Non-equilibrium dynamics of Dyson's model with an infinite number of particles
• Infinite-dimensional stochastic differential equations related to random matrices
• Infinite-dimensional stochastic differential equations and tail \(\sigma\)-fields
• Continuum limits of random matrices and the Brownian carousel
• Multilevel Dyson Brownian motions via Jack polynomials
• Strong Markov property of determinantal processes with extended kernels
• Zeros of Airy function and relaxation process
• Gradient dynamics of infinite point systems
• Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials. II: Airy random point field
• Interacting Brownian motions in infinite dimensions with logarithmic interaction potentials
• Cores of Dirichlet forms related to random matrix theory
• Brownian Gibbs property for Airy line ensembles
• THE KARDAR–PARISI–ZHANG EQUATION AND UNIVERSALITY CLASS
• An Introduction to Random Matrices
• A Brownian-Motion Model for the Eigenvalues of a Random Matrix
• Unendlich-dimensionale Wienerprozesse mit Wechselwirkung
• Unendlich-dimensionale Wienerprozesse mit Wechselwirkung

This page was built for publication: Infinite dimensional stochastic differential equations for Dyson's model