Infinite dimensional stochastic differential equations for Dyson’s model

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In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional stochastic differential equation (SDE) corresponding to the bulk limit of Dyson’s Brownian Motion, for all β≥ 1. Our construction applies to an explicit and general class of initial conditions, including the lattice configuration { xi} = Z and the sine process. We further show the convergence of the finite to infinite-dimensional SDE. This convergence concludes the determinantal formula of Katori and Tanemura (Commun Math Phys 293(2):469–497, 2010) for the solution of this SDE at β= 2.

Original languageEnglish (US)
Pages (from-to)801-850
Number of pages50
JournalProbability Theory and Related Fields
Issue number3-4
StatePublished - Dec 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Correlation function
  • Dyson’s Brownian motion
  • Dyson’s model
  • Infinite-dimensional
  • Pathwise uniqueness
  • Stochastic differential equations
  • Strong existence


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