Brunet-Derrida behavior of branching-selection particle systems on the line
The authors consider a class of branching-selection particle systems on \(R\) similar to the one considered by \textit{E. Brunet} and \textit{B. Derrida} [Computer Phys. Commun. 121--122, 376--381 (1999)] and give a rigorous mathematical proof 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 \( (\log N)^{-2}\).
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