Stability on {0,1,2,...}^S: birth-death chains and particle systems

TL;DR

This paper extends the concept of stability, a negative dependence property, from binary measures to reaction-diffusion processes and independent Markov chains, providing characterizations for birth-death chains that preserve this property.

Contribution

It generalizes the stability property to broader stochastic processes and characterizes birth-death chains that maintain stability in one dimension.

Findings

Stability property extended to reaction-diffusion processes and Markov chains.

Characterization of birth-death chains preserving stability in one dimension.

Connections established between stability and zero sets of generating functions.

Abstract

A strong negative dependence property for measures on {0,1}^n - stability - was recently developed in [5], by considering the zero set of the probability generating function. We extend this property to the more general setting of reaction-diffusion processes and collections of independent Markov chains. In one dimension the generalized stability property is now independently interesting, and we characterize the birth-death chains preserving it.