Local limit theorem in deterministic systems (1905.05164v1)

Abstract: We show that for every ergodic and aperiodic probability preserving system, there exists a $\mathbb{Z}$ valued, square integrable function $f$ such that the partial sums process of the time series $\left{f\circ T^i\right}_{i=0}^\infty$ satisfies the lattice local limit theorem.