A modified version of frozen percolation on the binary tree
نویسنده
چکیده
We consider the following, intuitively described process: at time zero, all sites of a binary tree are at rest. Each site becomes activated at a random uniform [0, 1] time, independent of the other sites. As soon as a site is in an infinite cluster of activated sites, this cluster of activated sites freezes. The main question is whether a process like this exists. Aldous [Ald00] proved that this is the case for a slightly different version of frozen percolation. In this paper we construct a process that fits the intuitive description and discuss some properties.
منابع مشابه
The Percolation Process on a Tree Where In niteClusters are
Modify the usual percolation process on the innnite binary tree by forbidding innnite clusters to grow further. The ultimate connguration will consist of both innnite and nite clusters. We give a rigorous construction of a version of this process and show that one can do explicit calculations of various quantities, for instance the law of the time (if any) that the cluster containing a xed edge...
متن کاملTwo-dimensional volume-frozen percolation: exceptional scales
We study a percolation model on the square lattice, where clusters “freeze” (stop growing) as soon as their volume (i.e. the number of sites they contain) gets larger than N , the parameter of the model. A model where clusters freeze when they reach diameter at least N was studied in [14, 6]. Using volume as a way to measure the size of a cluster – instead of diameter – leads, for large N , to ...
متن کاملA model for modified electrode with carbon nanotube composites using percolation theory in fractal space
We introduce a model for prediction the behavior of electrodes which modified withcarbon nanotubes in a polymer medium. These kinds of polymer composites aredeveloped in recent years, and experimental data for its percolation threshold isavailable. We construct a model based on percolation theory and fractal dimensionsand using experimental percolation threshold for calculating the moments of c...
متن کاملBivariate Uniqueness and Endogeny for Recursive Distributional Equations : Two Examples
In this work we prove the bivariate uniqueness property for two “maxtype” recursive distributional equations which then lead to the proof of endogeny for the associated recursive tree processes. Thus providing two concrete instances of the general theory developed by Aldous and Bandyopadhyay [3]. The first example discussed here deals with the construction of a frozen percolation process on a i...
متن کاملConnecting Yule Process, Bisection and Binary Search Tree via Martingales
We present new links between some remarkable martingales found in the study of the Binary Search Tree or of the bisection problem, looking at them on the probability space of a continuous time binary branching process.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005