On the birth-and-assassination process, with an application to scotching a rumor in a network

TL;DR

This paper introduces new formulas for the total particles in a birth-and-assassination process, proves its heavy-tailed distribution, and links it to rumor scotching and predator-prey dynamics as a scaling limit.

Contribution

It provides novel formulas and distribution analysis for the birth-and-assassination process and connects it to rumor scotching and predator-prey models.

Findings

Total number of particles has a heavy-tailed distribution.

The process is a scaling limit of rumor scotching in networks.

Related to predator-prey dynamics.

Abstract

We give new formulas on the total number of born particles in the stable birth-and-assassination process, and prove that it has an heavy-tailed distribution. We also establish that this process is a scaling limit of a process of rumor scotching in a network, and is related to a predator-prey dynamics.