Asymptotic normality of fringe subtrees and additive functionals in conditioned Galton–Watson trees1. Issue 1 (13th August 2014)

• Record Type: Journal Article
• Authors: Janson, Svante
• Is Part Of: Random structures & algorithms. Volume 48:Issue 1(2016)
• Page Start: 57
• Page End: 101
• Publication Date: 2014-08-13
• Subjects: fringe subtrees -- conditioned Galton‐Watson trees -- additive functionals -- toll functions; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20568
• Languages: English
• ISSNs: 1042-9832

Abstract

ABSTRACT: We consider conditioned Galton–Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe subtrees isomorphic to any given tree, and joint asymptotic normality for several such subtree counts. Another example is the number of protected nodes. The offspring distribution defining the random tree is assumed to have expectation 1 and finite variance; no further moment condition is assumed. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 57–101, 2016