One-dimensional Poisson growth models with random and asymmetric growth
type: Item
instance of: scholarly article
title: One-dimensional Poisson growth models with random and asymmetric growth
zbMATH Open document ID: 1029.60005
DOI: 10.1023/A:1022585818488
author: Fred W. Huffer
published in: Methodology and Computing in Applied Probability
publication date: 2003-05-27T00:00:00Z
review text: The following growth model is considered. There is a Poisson point process of germs on the line. Starting at time zero, a grain begins to grow from each germ point \(X_i\) at rates \(A_i\) to the left and \(B_i\) to the right where \(A_i, B_i\) are random variables. A grain stops growing when it touches another grain. Under various assumptions on the pairs \((A_i, B_i)\), several characteristics of this coverage process are obtained such as the fraction of the uncovered line, clumps' length distribution, etc. These results follow from similar theorems for growth processes on a circle. Additionally, simulation case study is performed.
reviewed by: Evgeny Spodarev
Mathematics Subject Classification ID: 60D05
Mathematics Subject Classification ID: 60G55
zbMATH DE Number: 1917926
zbMATH Keywords: germ-grain model
zbMATH Keywords: Poisson process
zbMATH Keywords: non-overlapping grains
zbMATH Keywords: growth process
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1917926