Anna graduated from the University of St Andrews with an MMath in Mathematics. In her final year Anna concentrated on Statistics for which she was awarded a Medal and the Duncan Prize. Her honours project was on Fractal aspects of Brownian motion and its generalisations, under the supervision of Prof Kenneth Falconer. Anna undertook internships in journalism, marketing, scientific research and political advisory. Her other interests include swimming, playing tennis and learning Mandarin.

Research project title:
Condensation in reinforced branching processes with fitness

Supervisor(s):
Peter Mörters, Cécile Mailler

Project description:
Anna studied a stochastic model for evolution of a structured population of particles equipped with fitness values. Each particle reproduces independently, with rate given by its fitness, and its offspring either inherits the fitness with some probability, or gets a new fitness value drawn from some probability distribution, independent of everything else. The particles of the same fitness are referred to as families. This is a stochastic version of Kingman’s model for population undergoing selection and mutation. However this framework also covers a dynamic random graph model, preferential attachment tree with fitness of Bianconi and Barabási, which is suitable for describing growth characteristics of real-life networks, such as social networks. There are two growth scenarios of the system: growth driven by bulk behaviour and growth driven by extremal behaviour (condensation case). Furthermore, there are two types of condensation: non- extensive, when no individual family makes an asymptotically positive contribution to the population, and macroscopic, when proportion of individuals in the largest family is asymptotically positive. Behaviour of the system is largely determined by properties of the chosen probability distribution. In this project, Anna focused on asymptotic behaviour of maximal families for bounded fitness distributions with a faster decay at the maximal fitness value. She established which of the above scenarios prevailed by drawing links with extreme value theory.