A Variational Approach to Branching Random Walk in Random Environment

Baillon JB, Clément PPJE, Greven A, den Hollander F (1993)

Publication Language: English

Publication Type: Journal article, Original article

Publication year: 1993

Journal

Annals of Probability Institute of Mathematical Statistics (IMS)

Publisher: Institute of Mathematical Statistics (IMS)

Book Volume: 21

Pages Range: 290-317

Journal Issue: 1

URI: https://projecteuclid.org/euclid.aop/1176989405

DOI: 10.1214/aop/1176989405

Abstract

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.

Authors with CRIS profile

Andreas Greven Lehrstuhl für Mathematische Stochastik

Involved external institutions

University of Paris 4 - Paris-Sorbonne / Université paris IV Paris-Sorbonne FR France (FR) Leiden University NL Netherlands (NL) Delft University of Technology (TU Delft) NL Netherlands (NL)

How to cite

APA:

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

MLA:

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

BibTeX: Download