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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
Galton-Watson Tree Mathematics
Branching Mathematics

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Projects 2013 2021

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

Research Output 2009 2019

  • 18 Article
  • 1 Conference contribution

The coalescent structure of continuous-time Galton-Watson trees

Harris, S., Johnston, S. & Roberts, M., 4 Sep 2019, (Accepted/In press) In : Annals of Applied Probability. 44 p.

Research output: Contribution to journalArticle

Open Access
File
Galton-Watson Tree
Continuous Time
Explicit Formula
Birth-death Process
Time Change
16 Downloads (Pure)

Mixing time bounds via bottleneck sequences

Addario-Berry, L. & Roberts, M., 1 Nov 2018, In : Journal of Statistical Physics. 173, 3-4, p. 845-871 27 p.

Research output: Contribution to journalArticle

Open Access
File
Mixing Time
Markov chains
Total Variation
Isometric
Isometry
1 Citation (Scopus)
20 Downloads (Pure)
Open Access
File
Branching Random Walk
Scaling Limit
Pareto
Poisson Point Process
Random Potential
2 Citations (Scopus)

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
11 Citations (Scopus)
65 Downloads (Pure)

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

Thesis

Spine Changes of Measure and Branching Diffusions

Author: Roberts, M., 1 Jun 2010

Supervisor: Harris, S. (Supervisor)

Student thesis: Doctoral ThesisPhD

File

The coalescent structure of continuous-time Galton-Watson trees

Author: Johnston, S., 9 Feb 2018

Supervisor: Roberts, M. (Supervisor) & Harris, S. (Supervisor)

Student thesis: Doctoral ThesisPhD

File