Mathematical Research Letters

Volume 18 (2011)

Number 3

Spectral analysis of random walk operators on euclidean space

Pages: 405 – 424

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n3.a2

Authors

Colin Guillarmou (Département de Mathématiques et Applications, École Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France)

Laurent Michel (Laboratoire J.-A. Dieudonné, Université de Nice, Parc Valrose, 06000 Nice, France)

Abstract

We study the operator associated to a random walk on $\R^d$ endowed with a probability measure. We give a precise description of the spectrum of the operator near $1$ and use it to estimate the total variation distance between the iterated kernel and its stationary measure. Our study contains the case of Gaussian densities on $\R^d$.

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