First order transition for the branching random walk at the critical parameter

Thomas Madaule

Stochastic Processes and their Applications, 2016, vol. 126, issue 2, 470-502

Abstract: Consider a branching random walk on the real line in the boundary case. The associated additive martingales can be viewed as the partition function of a directed polymers on a disordered tree. By studying the law of the trajectory of a particle chosen under the polymer measure, we establish a first order transition for the partition function at the critical parameter. This result is strongly related to the paper of Aïdékon and Shi (2014) in which they solved the problem of the normalization of the partition function in the critical regime.

Keywords: Branching random walk; Derivative martingale; Phase transition (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414915002264
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:126:y:2016:i:2:p:470-502

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2015.09.008

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().