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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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Projects

  • Research Output

    • 18 Article
    • 1 Conference contribution

    The coalescent structure of continuous-time Galton-Watson trees

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

    Research output: Contribution to journalArticle

  • 10 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
  • 26 Downloads (Pure)
    Open Access
    File
  • 1 Citation (Scopus)
    30 Downloads (Pure)

    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
  • 2 Citations (Scopus)

    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
  • 13 Citations (Scopus)
    94 Downloads (Pure)

    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