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SPECTRAL ANALYSIS OF HYPOELLIPTIC RANDOM WALKS

Published online by Cambridge University Press:  08 May 2014

Gilles Lebeau
Affiliation:
Laboratoire J.-A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France (lmichel@unice.fr; lebeau@unice.fr)
Laurent Michel
Affiliation:
Laboratoire J.-A. Dieudonné, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice Cedex 02, France (lmichel@unice.fr; lebeau@unice.fr)

Abstract

We study the spectral theory of a reversible Markov chain This random walk depends on a parameter $h\in ]0,h_{0}]$ which is roughly the size of each step of the walk. We prove uniform bounds with respect to $h$ on the rate of convergence to equilibrium, and the convergence when $h\rightarrow 0$ to the associated hypoelliptic diffusion.

Type
Research Article
Copyright
© Cambridge University Press 2014 

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