Automorphisms of the type II_1 Arveson system of Warren's noise

TL;DR

This paper investigates the automorphisms of Warren's noise Arveson system, showing that certain symmetries like rotations cannot be extended from simpler noise models to this more complex type II system.

Contribution

It demonstrates a fundamental limitation in extending rotational symmetries from white noise to Warren's noise within the Arveson system framework.

Findings

Rotations of the plane do not extend to Warren's noise system.

Automorphisms of type I systems differ from those of type II systems.

Certain symmetries are inherently incompatible with Warren's noise.

Abstract

Motions of the plane (shifts and rotations) correspond to automorphisms of the type I Arveson system of white noise. I prove that automorphisms corresponding to rotations cannot be extended to the type II Arveson system of Warren's noise.