Brunet-Derrida behavior of branching-selection particle systems on the line

DOI10.1007/S00220-010-1067-YzbMATH Open1247.60124arXiv0811.2782OpenAlexW2592832780MaRDI QIDQ1958541

Author name not available (Why is that?)

Publication date: 4 October 2010

Published in: (Search for Journal in Brave)

Abstract: We consider a class of branching-selection particle systems on $R$ 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 $(logN{)}^{-2}$. 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.

Full work available at URL: https://arxiv.org/abs/0811.2782

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Brunet-Derrida behavior of branching-selection particle systems on the line

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1958541)