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Products of Beta matrices and sticky flows
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  • Published: 25 May 2004

Products of Beta matrices and sticky flows

  • Y. Le Jan1 &
  • S. Lemaire1 

Probability Theory and Related Fields volume 130, pages 109–134 (2004)Cite this article

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  • 13 Citations

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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.

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References

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Authors and Affiliations

  1. Université Paris-Sud, Laboratoire de Mathématique, Bâtiment 425, 91405, Orsay cedex, France

    Y. Le Jan & S. Lemaire

Authors
  1. Y. Le Jan
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  2. S. Lemaire
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Correspondence to Y. Le Jan.

Additional information

Mathematics Subject Classification (2000):60J27, 60J35, 60G09

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Cite this article

Le Jan, Y., Lemaire, S. Products of Beta matrices and sticky flows. Probab. Theory Relat. Fields 130, 109–134 (2004). https://doi.org/10.1007/s00440-004-0358-7

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  • Received: 07 October 2002

  • Revised: 10 March 2004

  • Published: 25 May 2004

  • Issue Date: September 2004

  • DOI: https://doi.org/10.1007/s00440-004-0358-7

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Keywords

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