Joining primeness and disjointness from infinitely divisible systems

TL;DR

This paper investigates the relationships between ergodic systems generated by infinitely divisible processes and other systems, revealing disjointness properties related to spectral types and system classifications.

Contribution

It establishes new disjointness results between infinitely divisible stationary processes and certain classes of dynamical systems based on spectral properties.

Findings

Ergodic systems from infinitely divisible processes are disjoint from distally simple systems.

Such systems are also disjoint from systems with singular maximal spectral types.

The results connect spectral measures with disjointness in ergodic theory.

Abstract

We show that ergodic dynamical systems generated by infinitely divisible stationary processes are disjoint in the sense of Furstenberg with distally simple systems and systems whose maximal spectral type is singular with respect to the convolution of any two continuous measures.