On Mixing of Staircase Transformations

TL;DR

This paper proves that all staircase transformations satisfying certain growth conditions are mixing, advancing the understanding of their long-term statistical behavior in ergodic theory.

Contribution

It establishes mixing for staircase transformations under specific conditions, extending previous results in ergodic theory.

Findings

Proved mixing for staircase transformations with $r_j/h_j o 0$ and $r_j oty$

Extended the class of known mixing transformations

Provided new conditions ensuring ergodic properties

Abstract

We prove the mixing for all staircase transformations satisfied the conditions $r_j/h_j\to 0$ + $r_j\to\infty$.