%0 Journal Article
%T A Necessary and Sufficient Condition for the Tail-Triviality of a Recursive Tree Process
%A Antar Bandyopadhyay
%J Mathematics
%D 2005
%I arXiv
%X Given a recursive distributional equation (RDE) and a solution $\mu$ of it, we consider the tree indexed invariant process called the recursive tree process (RTP) with marginal $\mu$. 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.
%U http://arxiv.org/abs/math/0511203v2