Projects per year

## Personal profile

### Research interests

My research is in probability, and concentrates mainly on systems with an underlying branching structure.

This includes traditional mathematical models such as branching Brownian motion and Galton-Watson trees. We imagine a system of organisms, each of which moves around in space, breeds and eventually dies. Does the population survive forever, or eventually die out? How quickly does it colonise space?

It turns out that these mathematical questions have some surprising applications, and I am also interested in ways of using branching models to study other objects: computer algorithms, mutation rates in evolutionary biology, and mixing times for Markov chains, to name a few examples.

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## Projects 2013 2021

### UR Fellowship - Spacial Dependence in Branching Structures

1/10/16 → 30/09/21

Project: Research council

### EPSRC Posdoctoral Fellowship in Applied Probability for Dr Matthew I Roberts

3/04/13 → 2/07/16

Project: Research council

## Research Output 2009 2018

### Mixing time bounds via bottleneck sequences

Addario-Berry, L. & Roberts, M., 1 Nov 2018, In : Journal of Statistical Physics. 173, 3-4, p. 1-27 27 p.Research output: Contribution to journal › Article

### Scaling limit and ageing for branching random walk in Pareto environment

Ortgiese, M. & Roberts, M., 11 Jul 2018, In : Annales de l'Institut Henri Poincaré: Probabilités et Statistiques. 54, 3, p. 1291-1313Research output: Contribution to journal › Article

### One-point localization for branching random walk in Pareto environment

Ortgiese, M. & Roberts, M., 17 Jan 2017, In : Electronic Journal of Probability. 22, 20 p., 6.Research output: Contribution to journal › Article

### The many-to-few lemma and multiple spines

Harris, S. & Roberts, M., 8 Feb 2017, In : Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. 53, 1, p. 226-242Research output: Contribution to journal › Article

### Vanishing corrections for the position in a linear model of FKPP fronts

Berestycki, J., Brunet, É., Harris, S. & Roberts, M., 30 Jan 2017, In : Communications in Mathematical Physics. 349, 3, p. 857-893 37 p.Research output: Contribution to journal › Article

## Thesis

## Spine Changes of Measure and Branching Diffusions

Author: Roberts, M., 1 Jun 2010Supervisor: Harris, S. (Supervisor)

Student thesis: Doctoral Thesis › PhD

## The coalescent structure of continuous-time Galton-Watson trees

Author: Johnston, S., 9 Feb 2018Supervisor: Roberts, M. (Supervisor) & Harris, S. (Supervisor)

Student thesis: Doctoral Thesis › PhD