The shape of multidimensional Brunet-Derrida particle systems

DOI10.1214/14-AAP1062zbMATH Open1391.60230arXiv1305.0254OpenAlexW2962684260WikidataQ129998162 ScholiaQ129998162MaRDI QIDQ1650087

Author name not available (Why is that?)

Publication date: 29 June 2018

Published in: (Search for Journal in Brave)

Abstract: We introduce particle systems in one or more dimensions in which particles perform branching Brownian motion and the population size is kept constant equal to $N>1$, through the following selection mechanism: at all times only the $N$ fittest particles survive, while all the other particles are removed. Fitness is measured with respect to some given score function $s:R^{d}oR$. For some choices of the function $s$, it is proved that the cloud of particles travels at positive speed in some possibly random direction. In the case where $s$ is linear, we show under some assumptions on the initial configuration that the shape of the cloud scales like $logN$ in the direction parallel to motion but at least $c(logN{)}^{3/2}$ in the orthogonal direction for some $c>0$. We conjecture that the exponent 3/2 is sharp. This result is equivalent to the following result of independent interest: in one-dimensional systems, the genealogical time is greater than $c(logN{)}^3$, thereby contributing a step towards the original predictions of Brunet and Derrida. We discuss several open problems and also explain how our results can be viewed as a rigorous justification of Weismann's arguments for the role of recombination in population genetics.

Full work available at URL: https://arxiv.org/abs/1305.0254

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: The shape of multidimensional Brunet-Derrida particle systems

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1650087)