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arXiv · 1304.0562

Speed and fluctuations of N-particle branching Brownian motion with spatial selection

Pascal Maillard
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Abstract

We consider branching Brownian motion on the real line with the following selection mechanism: Every time the number of particles exceeds a (large) given number $N$, only the $N$ right-most particles are kept and the others killed. After rescaling time by $\log^3N$, we show that the properly recentred position of the $\lceil αN\rceil$-th particle from the right, $α\in(0,1)$, converges in law to an explicitly given spectrally positive Lévy process. This behaviour has been predicted to hold for a large class of models falling into the universality class of the FKPP equation with weak multiplicative noise [Brunet et al., Phys. Rev. E \textbf{73}(5), 056126 (2006)] and is proven here for the first time for such a model.

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Pascal Maillard. 2018-06-19. Speed and fluctuations of N-particle branching Brownian motion with spatial selection. https://doi.org/10.1007/s00440-016-0701-9

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