Diffusive behavior of ergodic sums over rotations

Conze, J.-P. ✉; Isola, S. ✉; Le, Borgne S.

Angol nyelvű Tudományos Szakcikk (Folyóiratcikk)
Megjelent: STOCHASTICS AND DYNAMICS 0219-4937 19 (2) Paper: 1950016 2019
  • SJR Scopus - Modeling and Simulation: Q2
For a rotation by an irrational α on the circle and a BV function φ, we study the variance of the ergodic sums S Lφ (x):=σ j=0 L-1 φ(x + jα). When α is not of constant type, we construct sequences (LN) such that, at some scale, the ergodic sums SLNφ satisfy an ASIP. Explicit non-degenerate examples are given with an application to the rectangular periodic billiard in the plane. © 2019 World Scientific Publishing Company.
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2020-08-05 01:57