Yazar
Öz, Mehmet
Basım Tarihi
2020
Basım Yeri
-
Instituto Nacional de Matematica Pura e Aplicada
Konu
Branching Brownian motion, Large deviations, Local mass, Local growth
Tür
Süreli Yayın
Dil
İngilizce
Dijital
Evet
Yazma
Hayır
Kütüphane
Özyeğin Üniversitesi
Demirbaş Numarası
1980-0436
Kayıt Numarası
642d6729-a251-4400-bf72-6aa4bf0407f5
Lokasyon
Natural and Mathematical Sciences
Tarih
2020
Örnek Metin
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
