Typical Cluster Size for 2-Dim Percolation Processes.
Abstract
The purpose of this paper is to discuss some characteristics of the typical cluster size for the self-matching 2-dimensional percolation models. For simplicity the author only describes his results for the site percolation model on double Z squared and leaves the task of extending this discussion to general models to the readers. Let us now introduce the 2-dim site percolation model. Let P sub p denote the probability measure under which all sites of the lattice double Z squared are independently occupied (non-occupied) with probability p (respectively 1-p). It is said that x is connected to y if there is a nearest neighbor path over occupied sites connecting x and y. (Let W sub O = x is an element of double Z squared as O approaches x) the cluster of occupied sites connected to O. This paper is devoted to the study of certain special properties of the typical cluster size about the critical point (p sub c = inf(p : P sub p (O approaches infinity) > O)).
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1986
- Accession Number
- ADA185519
Entities
People
- Bao G. Nguyen
Organizations
- University of North Carolina at Chapel Hill