Spectral analysis of random walk operators on euclidian space

Colin Guillarmou (1) , Laurent Michel (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 JAD - Laboratoire Jean Alexandre Dieudonné

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 $\R^d$.

Domaines: Théorie spectrale [math.SP]

Colin Guillarmou, Laurent Michel. Spectral analysis of random walk operators on euclidian space. Mathematical Research Letters, 2011, 18 (3), pp.405-424. ⟨hal-00492441⟩