  Erdos-Renyi limit laws give the length scale of a time-window over which
time-averages in Birkhoff sums have a non-trivial almost-sure limit. We
establish Erdos-Renyi type limit laws for Holder observables on dynamical
systems modeled by Young Towers with exponential and polynomial tails. This
extends earlier results on Erdos-Renyi limit laws to a broad class of dynamical
systems with some degree of hyperbolicity.
