The Probability Group in the Statistics Department carries out research in random graphs and networks, random trees, branching processes, Lévy processes, interacting particle systems, queueing processes, models from statistical mechanics, coalescent processes and random walks. The Group's work is applied in population genetics, mathematical biology, network modelling and demography and there are natural intersections with the Stochastic Analysis Group, the Combinatorics Group and the Mathematical and Computational Finance Group in the Mathematics Institute.
Highlights in recent years include:
(i) Professor Etheridge and co-workers new approach to modelling biological populations evolving in two (or more) spatial continua which overcomes the longstanding obstruction identified by Felsenstein 1975 and dubbed by him the `pain in the torus' (Stochastic Models in Biological Sciences 2008, Electronic Journal of Probability 2010, Evolution 2010);
(ii) Professor Goldschmidt’s first detailed description and proof of the scaling limit of the Erdos-Renyi random graph at its critical point (Electronic Journal of Probability 2010, PTRF 2012), and her description of behaviour near the extinction time for an important family of fragmentation processes (AIHP 2010, best paper prize);
(iii) Professor Steinsaltz and collaborators’ new model for the evolution of complex traits depending on many sites (monograph in the Memoirs of the AMS) treats important open problems in the evolution of ageing
(iv) Professor Reinert has given a universality principle for homogeneous sums (Annals of Probability 2010) and introduced the general setup for the exchangeable pair coupling in a multivariate setting (Annals of Probability 2009);
(v) Professor McDiarmid’s new probabilistic and enumerative methods for analysing random graphs from a structured class (Combinatorics, Probability and Computing 2010, Random Structures and Algorithms 2012).
(vi) Professor Martin and co-workers' identification of a new correspondence between competition interfaces in a spatial growth model and `second class particles' in an exclusion process and its exploitation to identify a phase transition for the growth model and to calculate exact coexistence probabilities (Annals of Applied Probability 2009, AIHP 2009).
To find out more about research activity in Probability at Oxford (including details of probability workshops and other events), see the Oxford Probability webpage.
Professor Julien Berestycki
Professor Paul Chleboun
Professor Alison Etheridge
Professor Christina Goldschmidt
Professor James Martin
Professor Gesine Reinert
Professor David Steinsaltz
Dr Matthias Winkel
Dr Maria Christodoulou