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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Submitted on : Wednesday, June 30, 2004 - 6:22:02 PM
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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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