The minimum of a branching random walk outside the boundary case
Probability
2014-10-17 v2
Abstract
This paper is a complement to the studies on the minimum of a real-valued branching random walk. In the boundary case (Biggins, Kyprianou 2005), A\"{i}d\'ekon in a seminal paper (2013) obtained the convergence in law of the minimum after a suitable renormalization. We study here the situation when the log-generating function of the branching random walk explodes at some positive point and it cannot be reduced to the boundary case. In the associated thermodynamics framework this corresponds to a first order phase transition, while the boundary case corresponds to a second order phase transition.
Keywords
Cite
@article{arxiv.1406.6971,
title = {The minimum of a branching random walk outside the boundary case},
author = {Julien Barral and Yueyun Hu and Thomas Madaule},
journal= {arXiv preprint arXiv:1406.6971},
year = {2014}
}
Comments
35 pages, 3 figures