文章基本信息

标题：Generalized Divide and Color Models
本地全文：下载
作者：Jeffrey E. Steif ; Johan Tykesson
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2019
卷号：XVI
期号：2
页码：899-955
DOI：10.30757/ALEA.v16-33
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：In this paper, we initiate the study of “Generalized Divide and ColorModels”. A very interesting special case of this is the “Divide and Color Model”(which motivates the name we use) introduced and studied by Olle Häggström.In this generalized model, one starts with a finite or countable set V , a randompartition of V and a parameter p 2 [0; 1]. The corresponding Generalized Divideand Color Model is the f0; 1g-valued process indexed by V obtained by independently,for each partition element in the random partition chosen, with probabilityp, assigning all the elements of the partition element the value 1, and with probability1 􀀀 p, assigning all the elements of the partition element the value 0.Some of the questions which we study here are the following. Under what situationscan different random partitions give rise to the same color process? Whatcan one say concerning exchangeable random partitions? What is the set of productmeasures that a color process stochastically dominates? For random partitionswhich are translation invariant, what ergodic properties do the resulting color processeshave?The motivation for studying these processes is twofold; on the one hand, webelieve that this is a very natural and interesting class of processes that deservesinvestigation and on the other hand, a number of quite varied well-studied processesactually fall into this class such as (1) the Ising model, (2) the fuzzy Potts model,(3) the stationary distributions for the Voter Model, (4) random walk in randomscenery and of course (5) the original Divide and Color Model.
关键词：Exchangeable processes; ergodic theory; random partitions; stochastic;domination;