A Necessary and Sufficient Condition for the Tail-Triviality of a Recursive Tree Process
| dc.creator | Bandyopadhyay, Antar | |
| dc.date | 2005-11-08 | |
| dc.date | 2006-01-23 | |
| dc.date.accessioned | 2026-07-07T06:50:58Z | |
| dc.date.available | 2026-07-07T06:50:58Z | |
| dc.description | 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. | |
| dc.description | Minor changes in the wordings. 20 pages, 1 figure. To appear in Sankhya | |
| dc.identifier | https://arxiv.org/abs/math/0511203 | |
| dc.identifier | http://arxiv.org/abs/math/0511203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104837 | |
| dc.subject | Probability | |
| dc.subject | 60K35, 60G10, 60G20 | |
| dc.title | A Necessary and Sufficient Condition for the Tail-Triviality of a Recursive Tree Process | |
| dc.type | text |