Clustering statistics for sticky particles with Brownian initial velocity
type: Item
instance of: scholarly article
title: Clustering statistics for sticky particles with Brownian initial velocity
zbMATH Open document ID: 0959.60074
DOI: 10.1016/S0021-7824(00)00147-1
author: Jean Bertoin
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2000-06-22T00:00:00Z
review text: Consider a linear model of clustering of particles which evolves according to the Burgers equation: \(\partial_tu+ u\partial_xu= 0\), \(u(t,x)\) denoting the velocity at time \(t\) of the particle located at \(x\). This describes a model where (clusters of) particles which shock together aggregate, with conservation of mass and momentum. Start at \(t=0\) with uniform distribution of mass (on \(\mathbb{R}\)) and with Brownian distribution of velocities \(u(x,0)\) (on \(\mathbb{R}_+\)). The main result asserts that, conditionally on the state of the system at time \(t>0\), the masses of the clusters at time \(s< t\) are obtained by breaking into peaces each cluster of the time \(t\), independently of all locations and velocities and of the masses of the other clusters, the law of these peaces being governed by some precise Poisson measure on \(\mathbb{R}^*_+\). Moreover, as \(s\) decreases and \(t\) stays fixed, the above description of clusters evolves as a sequence of independent Brownian fragmentation processes, which is precisely related to the so-called standard additive coalescent.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 35Q53
zbMATH DE Number: 1463869
zbMATH Keywords: sticky particles
zbMATH Keywords: Brownian velocity
zbMATH Keywords: Burgers equation
zbMATH Keywords: coalescent
zbMATH Keywords: fragmentation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1463869