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

DOI10.1007/S00440-016-0701-9zbMATH Open1362.60075arXiv1304.0562OpenAlexW3104728431MaRDI QIDQ343801

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Publication date: 29 November 2016

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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 $lo{g}^{3}N$, we show that the properly recentred position of the $lceilalphaNceil$-th particle from the right, $alphain(0,1)$, converges in law to an explicitly given spectrally positive L'evy 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 extbf{73}(5), 056126 (2006)] and is proven here for the first time for such a model.

Full work available at URL: https://arxiv.org/abs/1304.0562

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