Open Access
March 2009 Tightness for a family of recursion equations
Maury Bramson, Ofer Zeitouni
Ann. Probab. 37(2): 615-653 (March 2009). DOI: 10.1214/08-AOP414


In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random walk in one dimension and the cover time of a symmetric simple random walk on regular binary trees. Recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers. Here, we use these recursion equations to establish the tightness of the corresponding sequences of distribution functions after appropriate centering. We phrase our results in a fairly general context, which we hope will facilitate their application in other settings.


Download Citation

Maury Bramson. Ofer Zeitouni. "Tightness for a family of recursion equations." Ann. Probab. 37 (2) 615 - 653, March 2009.


Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1169.60020
MathSciNet: MR2510018
Digital Object Identifier: 10.1214/08-AOP414

Primary: 39B12 , 60G50 , 60J80

Keywords: Branching random walk , Cover time , recursion equations , tightness

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 2 • March 2009
Back to Top