Chaotic tracial dynamics

TL;DR

This paper demonstrates that automorphisms of certain classifiable C*-algebras induce chaotic and weakly mixing dynamics on their trace spaces, with models illustrating statistical features like the central limit theorem.

Contribution

It establishes the chaotic nature of trace space dynamics for generic automorphisms and constructs models to observe statistical properties, advancing understanding of C*-algebra automorphisms.

Findings

Automorphisms induce chaotic trace dynamics

Models exhibit the central limit theorem and statistical features

Finite Rokhlin dimension relates to crossed product structures

Abstract

The action on the trace space induced by a generic automorphism of a suitable finite classifiable C*-algebra is shown to be chaotic and weakly mixing. Model C*-algebras are constructed to observe the central limit theorem and other statistical features of strongly chaotic tracial actions. Genericity of finite Rokhlin dimension is used to describe KK-contractible stably projectionless C*-algebras as crossed products.