Divergence of a stationary random vector field can be always positive (a Weiss' phenomenon)

TL;DR

This paper discusses a surprising phenomenon where the divergence of a stationary random vector field, typically centered, can almost surely equal 1, illustrating a counterintuitive property related to Weiss' 1997 discovery.

Contribution

It reveals that the divergence of stationary random vector fields can almost surely be positive, expanding understanding of their probabilistic behavior.

Findings

Divergence can be almost surely equal to 1

Contradicts the usual zero-mean assumption

Highlights Weiss' phenomenon in random fields

Abstract

The divergence of a stationary random vector field at a given point is usually a centered (that is, zero mean) random variable. Strangely enough, it can be equal to 1 almost surely. This fact is another form of a phenomenon disclosed by B. Weiss in 1997.