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.
Cite
@article{arxiv.math/0307106,
title = {Products of Beta matrices and sticky flows},
author = {Yves Le Jan and Sophie Lemaire},
journal= {arXiv preprint arXiv:math/0307106},
year = {2007}
}