Brunet-Derrida Behavior of Branching-Selection Particle Systems on the Line View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2010-09

AUTHORS

Jean Bérard, Jean-Baptiste Gouéré

ABSTRACT

We consider a class of branching-selection particle systems on similar to the one considered by E. Brunet and B. Derrida in their 1997 paper “Shift in the velocity of a front due to a cutoff”. Based on numerical simulations and heuristic arguments, Brunet and Derrida showed that, as the population size N of the particle system goes to infinity, the asymptotic velocity of the system converges to a limiting value at the unexpectedly slow rate (log N)−2. In this paper, we give a rigorous mathematical proof of this fact, for the class of particle systems we consider. The proof makes use of ideas and results by R. Pemantle, and by N. Gantert, Y. Hu and Z. Shi, and relies on a comparison of the particle system with a family of N independent branching random walks killed below a linear space-time barrier. More... »

PAGES

323-342

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-010-1067-y

DOI

http://dx.doi.org/10.1007/s00220-010-1067-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1048027638


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