Zsófia graduated from Budapest in 2018 with an MSc in mathematics, with special interest in probability and stochastics. As part of her Master’s studies she spent five months in Stockholm with the Erasmus+ program. In her Master’s thesis she worked out the proofs of two limit theorems about directed random polymer models. She also took part in two internships during her Master’s years, exploring a Markov model for reliability problems of telecommunications services and also financial models. Apart from math she likes to travel and to do sport, especially table tennis or tennis.

Research project title:
N-particle branching random walk

Supervisor(s):
Sarah Penington, Matt Roberts

Project description:
Branching random walks are well-studied models in probability theory. In particular, the Nparticle branching random walk (N-BRW), a branching random walk with selection, was first studied in the physics literature as a stochastic model for front propagation. In the N-BRW, at each time step, N particles have locations on the real line. Each of the N particles has two offspring, which have a random displacement from the location of their parent according to some fixed jump distribution. Then among the 2N offspring particles, only the N rightmost particles survive to form the next generation. The main purpose of Zsófia’s project is to explore the long-term behaviour of this process with different jump distributions. There has been substantial recent progress in this area, but many interesting questions remain, including the behaviour of the system when the jump distribution has stretched exponential tails.