The unscaled paths of branching Brownian motion

Simon C. Harris, Matthew I Roberts

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For a set A ⊂ C[0, ∞), we give new results on the growth of the number of particles in a branching Brownian motion whose paths fall within A. We show that it is possible to work without rescaling the paths. We give large deviations probabilities as well as a more sophisticated proof of a result on growth in the number of particles along certain sets of paths. Our results reveal that the number of particles can oscillate dramatically. We also obtain new results on the number of particles near the frontier of the model. The methods used are entirely probabilistic.
Original languageEnglish
Pages (from-to)579-608
Number of pages30
JournalAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques
Issue number2
Publication statusPublished - May 2012


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