2005/11/08 by Antar Bandyopadhyay, Bandyopadhyay, Antar
Computer Science · Mathematics · #60G10 #60G20 #60K35 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60G10 #msc:60G20 #msc:60K35
paper · pdf · doi:10.48550/arxiv.math/0511203
Minor changes in the wordings. 20 pages, 1 figure. To appear in Sankhya
openalex publication_date 2005/11/08 · arxiv created 2006/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a recursive distributional equation (RDE) and a solution μ of it, we consider the tree indexed invariant process called the recursive tree process (RTP) with marginal μ. We introduce a new type of bivariate uniqueness property which is different from the one defined by Aldous and Bandyopadhyay (2005), and we prove that this property is equivalent to tail-triviality for the RTP, thus obtaining a necessary and sufficient condition to determine tail-triviality for a RTP in general. As an application we consider Aldous' (2000) construction of the frozen percolation process on a infinite regular tree and show that the associated RTP has a trivial tail.