A universal divergence rate for symmetric Birkhoff Sums in infinite ergodic theory
classification
🧮 math.DS
keywords
birkhoffergodicinfinitesumssymmetrictheoryuniversaladdition
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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.
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