Spectral analysis of random walk operators on euclidean space

Colin Guillarmou (1) , Laurent Michel (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LJAD - 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: Equations aux dérivées partielles [math.AP]

Colin Guillarmou, Laurent Michel. Spectral analysis of random walk operators on euclidean space. Mathematical Research Letters, 2011, 18 (3), pp.405-424. ⟨10.4310/MRL.2011.v18.n3.a2⟩. ⟨hal-01343540⟩