Title: Potential kernel, hitting probabilities and distributional asymptotics,
Abstract: Z^d-extensions of probability-preserving dynamical systems are themselves
dynamical systems preserving an infinite measure, and generalize random walks.
Using the method of moments, we prove a generalized central limit theorem for
additive functionals of the extension of integral zero, under spectral
assumptions. As a corollary, we get the fact that Green-Kubo's formula is
invariant under induction. This allows us to relate the hitting probability of
sites with the symmetrized potential kernel, giving an alternative proof and
generalizing a theorem of Spitzer. Finally, this relation is used to improve in
turn the asumptions of the generalized central limit theorem. Applications to
Lorentz gases in finite horizon and to the geodesic flow on abelian covers of
compact manifolds of negative curvature are discussed.