Author
Öz, Mehmet
Publication Date
2020
Publication Place
-
Instituto Nacional de Matematica Pura e Aplicada
Subject
Branching Brownian motion, Large deviations, Local mass, Local growth
Type
Periodical
Language
English
Digital
Yes
Manuscript
No
Library
Özyeğin University
Library Asset ID
1980-0436
Record ID
642d6729-a251-4400-bf72-6aa4bf0407f5
Library Location
Natural and Mathematical Sciences
Date
2020
Sample Text
We study the local mass of a dyadic branching Brownian motion Z evolving in R-d. By 'local mass', we refer to the number of particles of Z that fall inside a ball with fixed radius and time-dependent center, lying in the region where there is typically exponential growth of particles. Using the strong law of large numbers for the local mass of branching Brownian motion and elementary geometric arguments, we find large deviation results giving the asymptotic behavior of the probability that the local mass is atypically small on an exponential scale. As corollaries, we obtain an asymptotic result for the probability of absence of Z in a ball with fixed radius and time-dependent center, and lower tail asymptotics for the local mass in a fixed ball. The proofs are based on a bootstrap argument, which we use to find the lower tail asymptotics for the mass outside a ball with time-dependent radius and fixed center, as well.
DOI
10.30757/ALEA.v17-27
Cilt
17
