Mathematical Research Letters
Volume 18 (2011)
Spectral analysis of random walk operators on euclidean space
Pages: 405 – 424
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 $\R^d$.