On the incipient cluster of the binary tree
type: Item
instance of: scholarly article
title: On the incipient cluster of the binary tree
zbMATH Open document ID: 0807.60088
DOI: 10.1007/BF01196678
author: Hermann Haase
published in: Archiv der Mathematik
publication date: 1995-02-28T00:00:00Z
review text: We consider the subcritical percolation process on a binary tree and prove the existence of a probability measure \(\nu_ p\) such that \(\nu_ p\)-almost surely the open cluster of the root of the binary tree is infinite. At the percolation threshold it looks like a single thread having a lot of finite branches.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B43
zbMATH DE Number: 701025
zbMATH Keywords: subcritical percolation process
zbMATH Keywords: binary tree
zbMATH Keywords: percolation threshold
MaRDI profile type: Publication
cites work: Defining Fractal Subsets of Z d
cites work: Some general results concerning the critical exponents of percolation processes
cites work: Random walk on the infinite cluster of the percolation model
cites work: Q5727090
cites work: Q4118602
cites work: Q3672870
cites work: Scaling relations for 2D-percolation
cites work: Random walks and percolation on trees
cites work: Random walk in a random environment and first-passage percolation on trees
full work available at URL: https://doi.org/10.1007/bf01196678
OpenAlex ID: W2077518662
description: scientific article; zbMATH DE number 701025