We analyze whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the increment x(t,T)=x(t+T)−x(t), e.g. x(t,T)=ln(p(t+T)/p(t)) in finance...

A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in Rn, or Sn,n∈N, which are distributed according to the configurational microcanonical measure δ(E−H), or rather some regularization thereof, where H is the...