A universal divergence rate for symmetric Birkhoff Sums in infinite   ergodic theory
  We show that there exists a universal gap in the failure of the ergodic theorem for symmetric Birkhoff sums in infinite ergodic theory. In addition, an application of this result to a question of fluctuations of the Birkhoff integrals of horocyclic flows on geometrically finite surfaces is given. 
Zemer Kosloff
math.DS