Abstract
We show that for every ergodic and aperiodic probability preserving system, there exists an integer valued square integrable function whose Birkhoff sums process satisfies the lattice local limit theorem.
On montre que dans tout système dynamique probabilisé ergodique et apériodique, il existe une fonction de carré intégrable à valeurs entières dont les sommes de Birkhoff satisfont le théorème limite local.
Funding Statement
The research of Z.K. is partially supported by ISF grant no. 1570/17.
Dedication
Dedicated to Manfred Denker whose work is an inspiration for us.
Citation
Zemer Kosloff. Dalibor Volny. "Local limit theorem in deterministic systems." Ann. Inst. H. Poincaré Probab. Statist. 58 (1) 548 - 566, February 2022. https://doi.org/10.1214/21-AIHP1169
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