Galton-Watson Trees with the Same Mean Have the Same Polar Sets
| dc.creator | Pemantle, Robin | |
| dc.creator | Peres, Yuval | |
| dc.date | 2004-04-02 | |
| dc.date.accessioned | 2026-07-07T05:07:03Z | |
| dc.date.available | 2026-07-07T05:07:03Z | |
| dc.description | Evans defines a notion of what it means for a set B to be polar for a process indexed by a tree. The main result herein is that a tree picked from a Galton-Watson measure whose offspring distribution has mean m and finite variance will almost surely have precisely the same polar sets as a deterministic tree of the same growth rate. This implies that deterministic and nondeterministic trees behave identically in a variety of probability models. Mapping subsets of Euclidean space to trees and polar sets to capacity criteria, it follows that certain random Cantor sets are capacity-equivalent to each other and to deterministic Cantor sets. An extension to branching processes in varying environment is also obtained. | |
| dc.description | 30 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404053 | |
| dc.identifier | http://arxiv.org/abs/math/0404053 | |
| dc.identifier | Ann. Probab., 23, 1102 - 1124 (1995) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70709 | |
| dc.subject | Probability | |
| dc.subject | 60J80, 60J45 (Primary) 60D05, 60G60 (Secondary) | |
| dc.title | Galton-Watson Trees with the Same Mean Have the Same Polar Sets | |
| dc.type | text |