A Variational Approach to Branching Random Walk in Random Environment

Journal article
(Original article)

Publication Details

Author(s): Baillon JB, Clément PPJE, Greven A, den Hollander F
Journal: Annals of Probability
Publisher: Institute of Mathematical Statistics (IMS)
Publication year: 1993
Volume: 21
Journal issue: 1
Pages range: 290-317
ISSN: 0091-1798
Language: English


This paper considers an infinite system of particles on the integers Z" role="presentation">ℤ
that: (1) step to the right with a random delay, and (2) split or die
along the way according to a random law depending on their position. The
exponential growth rate of the particle density is computed in the long
time limit in the form of a variational formula that can be solved
explicitly. The result reveals two phase transitions associated with
localization vs. delocalization and survival vs. extinction. In
addition, the system exhibits an intermittency effect. Greven and den
Hollander considered the more difficult situation where the particles
may step both to the left and right, but the analysis of the phase
diagram was less complete.

FAU Authors / FAU Editors

Greven, Andreas Prof. Dr.
Lehrstuhl für Stochastik

External institutions with authors

Delft University of Technology
Leiden University
University of Paris 4 - Paris-Sorbonne / Université paris IV Paris-Sorbonne

How to cite

Baillon, J.-B., Clément, P.P.J.E., Greven, A., & den Hollander, F. (1993). A Variational Approach to Branching Random Walk in Random Environment. Annals of Probability, 21(1), 290-317. https://dx.doi.org/10.1214/aop/1176989405

Baillon, Jean-Bernard, et al. "A Variational Approach to Branching Random Walk in Random Environment." Annals of Probability 21.1 (1993): 290-317.


Last updated on 2018-23-07 at 16:10