Thesis Defense – Elif Aydoğan (MSMATH)

Elif Aydoğan – M.Sc. Mathematics

Asst. Prof. Mehmet Öz – Advisor

Date: 14.05.2024

Time: 11.00

Location: AB1 238

  “BRANCHING BROWNIAN MOTION IN A TIME-DEPENDENT BALL”

Asst. Prof. Mehmet Öz, Özyeğin University

Asst. Prof.  Berkay Anahtarcı, Özyeğin University

Asst. Prof. Rukiye Kara, Mimar Sinan Fine Arts University

Abstract:

In this thesis, we study a d-dimensional branching Brownian motion (BBM) evolving inside a subdiffusively expanding ball. BBM is a randomly branching stochastic mathematical model where each particle moves under Brownian motion independently of each other. The particles of BBM are deactivated instantly upon touching the boundary of an expanding ball, but they can be reactivated at a later time provided their ancestral lines are fully inside the expanding ball at that later time. The main quantity of interest is the large-time mass of the BBM, that is, the number of active particles at a large time t inside this restricted domain. The study aims at obtaining sharp asymptotic results as time tends to infinity on the large-deviation probability that the mass inside the expanding ball is atypically small.

Bio:

Elif Aydoğan received her BS degree in Mathematics from Ege University in 2020. She is a graduate student in the Mathematics Program at Özyeğin University. Her research focuses on Probability Theory.