# Products of Beta matrices and sticky flows

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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https://hal.archives-ouvertes.fr/hal-00000491
Contributor : Sophie Lemaire <>
Submitted on : Wednesday, June 30, 2004 - 6:22:02 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM
Long-term archiving on : Thursday, September 23, 2010 - 3:15:10 PM

### Citation

Yves Le Jan, Sophie Lemaire. Products of Beta matrices and sticky flows. Probability Theory and Related Fields, Springer Verlag, 2004, 130 (1), pp.109-134. ⟨10.1007/s00440-004-0358-7⟩. ⟨hal-00000491v3⟩

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