The annihilating process
type: Item
instance of: scholarly article
title: The annihilating process
zbMATH Open document ID: 1001.60102
author: Martin O'Hely
author: Aidan Sudbury
published in: Journal of Applied Probability
publication date: 2002-12-04T00:00:00Z
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 1625619
zbMATH Keywords: infinite particle system
zbMATH Keywords: annihilation
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1239/jap/996986655
OpenAlex ID: W2092138355
DOI: 10.1239/JAP/996986655
review text: In this particle system the only interaction is that each particle kills a neighboring particle at a fixed rate. There is no birth and no movement, hence an isolated particle remains for ever. The authors show that when the initial configuration is the set of integers, the distribution of particles at all times is a renewal process and that the probability that a site remains occupied for all times converges to \(1/e\). Using a Harris graphical construction they describe explicitly the distribution of the renewal process for all times. They extend some of the results to a tree and leave open the problem in dimensions \(d\geq 2\).
reviewed by: Pablo A. Ferrari
description: scientific article; zbMATH DE number 1625619