Typical infinite mixing automorphisms are rank-one

TL;DR

This paper demonstrates that typical infinite mixing automorphisms are rank-one, extending previous results about finite cases using Sidon's constructions.

Contribution

It proves that generic infinite mixing automorphisms are rank-one, generalizing earlier finite case results with new constructions.

Findings

Generic infinite mixing automorphisms are rank-one.

Extension of finite case results to infinite automorphisms.

Use of Sidon's constructions in the proof.

Abstract

Bashtanov proved that generic mixing automorphisms of probability space with respect to the Alpern-Tikhonov metric had rank one. Using Sidon's constructions, we show that generic infinite mixing automorphisms also are rank-one.