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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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  • 4 Similar Profiles
Branching Brownian Motion Mathematics
Branching Random Walk Mathematics
Spine Mathematics
Branching process Mathematics
Pareto Mathematics
Path Mathematics
Branching Mathematics
Galton-Watson Tree Mathematics

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Projects 2013 2021

Component sizes of random graphs and noise sensitivity

Roberts, M.

1/10/1831/03/21

Project: Research council

Reimagining Recruitment

Rogers, T. & Roberts, M.

24/09/1823/09/20

Project: Research council

Spatial Fragmentations

Roberts, M.

2/10/171/10/20

Project: Research council

fragmentation
rectangles
rocks
atomic structure
avalanches
Brownian movement
DNA
Internet
Sorting
Molecules

Research Output 2009 2018

  • 16 Article
  • 2 Doctoral Thesis
  • 1 Conference contribution
Open Access
File
Branching Random Walk
Scaling Limit
Pareto
Poisson Point Process
Random Potential
1 Citations

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 journalArticle

Open Access
Branching Random Walk
Pareto
Anderson Model
Random Potential
Intermittency

The coalescent structure of continuous-time Galton-Watson trees

Johnston, S. G. G., 26 Sep 2017, 116 p.

Research output: ThesisDoctoral Thesis

Open Access
File
2 Citations

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. 226-242

Research output: Contribution to journalArticle

File
Many to one
Spine
Branching process
Intuitive
Lemma
3 Citations

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

Research output: Contribution to journalArticle

Open Access
File
Linear Model
Initial conditions
Term
Decay
Absorbing Boundary