Mixing on Stochastic Staircase Transformations

TL;DR

This paper proves mixing properties for a broad class of rank-one transformations, encompassing known and new constructions, thereby advancing the understanding of their ergodic behavior.

Contribution

It establishes mixing for a general class of rank-one transformations, including all known examples and new variants, unifying and extending previous results.

Findings

Proved mixing for all known rank-one transformations

Extended mixing results to new constructions

Unified understanding of rank-one transformation behavior

Abstract

We prove mixing on a general class of rank-one transformations containing all known examples of rank-one mixing, including staircase transformations and Ornstein's constructions, and a variety of new constructions.