Homogenization of a reflecting barrier Brownian motion in a continuum percolation cluster in \(R^ d\)
type: Item
instance of: scholarly article
title: Homogenization of a reflecting barrier Brownian motion in a continuum percolation cluster in \(R^ d\)
zbMATH Open document ID: 0808.60085
author: H. Tanemura
published in: Kodai Mathematical Journal
publication date: 1994-12-19T00:00:00Z
review text: A continuum percolation model in \(\mathbb{R}^ d\) \((d \geq 2)\), which is called the Poisson blob model, is considered. It should be viewed as a continuum analogue of the discrete site percolation model. Instead of sites being independently occupied we have a Poisson process with each Poisson point being the center of an occupied disc of radius \(r\). A central limit theorem is proven for a reflecting Brownian motion in an unbounded occupied cluster of the model in the supercritical case. For an unbounded vacant cluster of the model, a similar result is obtained in the subcritical case.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 701566
zbMATH Keywords: Poisson distribution
zbMATH Keywords: central limit theorem
zbMATH Keywords: continuum percolation model
zbMATH Keywords: discrete site percolation model
zbMATH Keywords: reflecting Brownian motion
zbMATH Keywords: supercritical case
zbMATH Keywords: subcritical case
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039962
OpenAlex ID: W2015344829
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DOI: 10.2996/KMJ/1138039962
description: scientific article; zbMATH DE number 701566