Erratum : “Pathwise approximations of process based on the fine structure of their filtrations”
Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.
The Varopoulos-Hardy-Littlewood theory and the spectral analysis are used to estimate the tail of the distribution of the first exit time of α-stable processes.
Convex records in Euclidean space are considered. We provide both lower and upper bounds on the probability that in a sequence of random vectors ,..., there are exactly k records.
We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential kernel.