The randomly fluctuating hyperrectangles are spatially monotone

TL;DR

This paper proves that in a one-dimensional process of randomly fluctuating hyperrectangles, the likelihood of a site being occupied diminishes monotonically as its distance from the origin increases.

Contribution

It establishes a monotonicity property of occupation probabilities in a specific stochastic spatial process, providing new insights into its spatial structure.

Findings

Occupation probability decreases with distance from the origin

Monotonicity holds at all time instances

Results apply to one-dimensional hyperrectangle processes

Abstract

We show that the probability of a site being occupied at any instance of time in the one-dimensional randomly fluctuating hyperrectangles processes decreases monotonically with respect to its distance from the origin.