2013/04/30 by Pascal Maillard · 1 citation
Mathematics · Physics and Astronomy · #Branching (polymer chemistry) #Brownian motion #Large deviations theory #Multiplicative function #Multiplicative noise #Particle system #Random Matrices and Applications #Real line #Stochastic process #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Universality (dynamical systems) #math-ph #math.AP #math.MP #math.PR #msc:60J70 #msc:60J80 #msc:60K35
paper · pdf · doi:10.1007/s00440-016-0701-9
published as Probability Theory and Related Fields, 166(3), 1061-1173, 2016 · Continues and essentially replaces arXiv:1112.0266v1. Based on Chapter 2 of my PhD thesis at Université Pierre et Marie Curie, Paris, available at arXiv:1210.3500. Changes in v2 (74 pages): Reorganisation, simplifications in some places, typos corrected. Changes in v3 (84 pages): Many small corrections and additional details. Changes in v4 (87 pages): journal version, minor modifications
crossref issued 2016/04/22 · crossref published 2016/04/22 · crossref published-online 2016/04/22 · openalex publication_date 2016/04/22 · crossref created 2016/04/22 · openalex created_date 2016/06/24 · crossref published-print 2016/12/01 · arxiv created 2018/06/19 · arxiv updated 2018/06/20 · crossref deposited 2022/05/09 · crossref indexed 2026/08/04 · openalex updated_date 2026/08/05
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 log3N, we show that the properly recentred position of the \lceil αN\rceil-th particle from the right, α∈(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 73(5), 056126 (2006)] and is proven here for the first time for such a model.