Translator Disclaimer
March 2009 Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees
Yueyun Hu, Zhan Shi
Ann. Probab. 37(2): 742-789 (March 2009). DOI: 10.1214/08-AOP419

Abstract

We establish a second-order almost sure limit theorem for the minimal position in a one-dimensional super-critical branching random walk, and also prove a martingale convergence theorem which answers a question of Biggins and Kyprianou [Electron. J. Probab. 10 (2005) 609–631]. Our method applies, furthermore, to the study of directed polymers on a disordered tree. In particular, we give a rigorous proof of a phase transition phenomenon for the partition function (from the point of view of convergence in probability), already described by Derrida and Spohn [J. Statist. Phys. 51 (1988) 817–840]. Surprisingly, this phase transition phenomenon disappears in the sense of upper almost sure limits.

Citation

Download Citation

Yueyun Hu. Zhan Shi. "Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees." Ann. Probab. 37 (2) 742 - 789, March 2009. https://doi.org/10.1214/08-AOP419

Information

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

zbMATH: 1169.60021
MathSciNet: MR2510023
Digital Object Identifier: 10.1214/08-AOP419

Subjects:
Primary: 60J80

Rights: Copyright © 2009 Institute of Mathematical Statistics

JOURNAL ARTICLE
48 PAGES


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