Galton-Watson trees with the same mean have the same polar sets

Galton-Watson trees with the same mean have the same polar sets (1995)

by Robin Pemantle , Yuval Peres

Venue:	ANN. PROBAB
Citations:	15 - 10 self

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Datum	Value	Source
TITLE	Galton-Watson trees with the same mean have the same polar sets	user correction
AUTHOR NAME	Robin Pemantle	user correction
AUTHOR NAME	Yuval Peres	user correction
AUTHOR AFFIL	Department of Statistics, Evans Hall, University of California, Berkeley	user correction
AUTHOR ADDR	CA 94720	user correction
ABSTRACT	Evans (1992) 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 also follows that certain random Cantor sets are capacity-equivalent to each other and to deterministic Cantor sets.	user correction
YEAR	1995	INFERENCE
VENUE	ANN. PROBAB	user correction
VENUE TYPE	JOURNAL	INFERENCE
CITATIONS	21 found	ParsCit 1.0