Products of Beta matrices and sticky flows

Y. Le Jan, S. Lemaire

Research output: Contribution to journalArticlepeer-review

Abstract

A discrete model of Brownian sticky flows on the unit circle is described: it is constructed with products of Beta matrices on the discrete torus. Sticky flows are defined by their "moments" which are consistent systems of transition kernels on the unit circle. Similarly, the moments of the discrete model form a consistent system of transition matrices on the discrete torus. A convergence of Beta matrices to sticky kernels is shown at the level of the moments. As the generators of the n-point processes are defined in terms of Dirichlet forms, the proof is performed at the level of the Dirichlet forms. The evolution of a probability measure by the flow of Beta matrices is described by a measure-valued Markov process. A convergence result of its finite dimensional distributions is deduced.

Original languageEnglish (US)
Pages (from-to)109-134
Number of pages26
JournalProbability Theory and Related Fields
Volume130
Issue number1
DOIs
StatePublished - Sep 2004

Keywords

  • Convergence of resolvents
  • Dirichlet forms
  • Dirichlet laws
  • Feller semigroups
  • Markov chains with continuous parameter
  • Polya urns
  • Stochastic flow of kernels

ASJC Scopus subject areas

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

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