I am an Associate Professor (University Lecturer) in the Department of Statistics and a Tutorial Fellow at Lady Margaret Hall in the University of Oxford.
departmental webpage and
I am a member of the Probability Group in the Department of
Find out more
about research activity
- How to find my office/contact me
- My departmental office is 50.22 in the Medawar Building
(number 37 on this map)
and my telephone number is (01865) (2)81224.
- My college office is on the ground floor at the back of 2
Fyfield Road and my telephone number there is (01865) (2)74392.
- Prelims Probability (Michaelmas Term
- APTS Applied Stochastic Processes (in Leeds, 4th-8th
August 2014): course
- I give tutorials on Prelims Probability, Prelims
Statistics, Prelims Optimisation, Part A Probability, Part
A Statistics and Part A Graph Theory to
the LMH students. These are held in my LMH office, on
the ground floor of 2 Fyfield Road.
- I act as a coursework supervisor for the MSc in
- I supervise Part C projects for Mathematics and
Statistics students and masters dissertations for the MSc
in Applied Statistics.
- In 2013, I supervised Benjamin Scellier of École
polytechnique for his stage de M1.
- Brief academic CV
- Research interests
- My research interests lie in probability and combinatorics. I
wrote my Ph.D. thesis on various aspects of the structure of random
hypergraphs, with particular emphasis on the use of stochastic process
methods. More recently, I have been working on scaling limits for
various random graphs. I have also worked extensively on processes of
coagulation (or coalescence) and fragmentation. Random trees and
branching processes have played a large part in this research. I am also interested in applications of
coalescence theory to mathematical population genetics. In a rather
different direction, I am interested in random satisfiability problems,
such as random K-SAT.
- Essays and theses
- My Part III (approximately masters-level) essay entitled The Chen-Stein Method for Convergence of
Distributions [.ps.gz (120kb)].
- My PhD thesis entitled Large Random
Hypergraphs [.ps.gz (747kb)].
- Published research papers and preprints
- Essential edges in Poisson random
hypergraphs, with James Norris, Random
Structures and Algorithms 24, 4 (2004) pp.381-396.
[.pdf, arXiv math.PR/0401143].
- Critical random hypergraphs: the
of a giant set of identifiable vertices, Annals of
Probability 33, 4 (2005) pp.1573-1600.
[.pdf, arXiv math.PR/0401208].
- Dual random fragmentation and
and an application to the genealogy of Yule processes,
Bertoin, in Mathematics and Computer Science III:
Algorithms, Trees, Combinatorics and Probabilities, M. Drmota,
P. Flajolet, D. Gardy, B. Gittenberger (Eds.) (2004) pp.295-308.
[.ps.gz, arXiv math.PR/0408128].
- Random recursive trees and the
Bolthausen-Sznitman coalescent, with James Martin,
Journal of Probability, 10 (2005), Paper no. 21, pp.718-745.
[.pdf, arXiv math.PR/0502263,
- Preservation of log-concavity on
summation, with Oliver Johnson, ESAIM:
Probability and Statistics 10 (2006) pp.206-215.
[.pdf, arXiv math.PR/05025848].
- Coagulation-fragmentation duality, Poisson-Dirichlet
distributions and random recursive trees, with Rui Dong and James
Martin, Annals of Applied
Probability, 16, 4 (2006) pp.1733-1750.
[.pdf, arXiv math.PR/0507591].
- Asymptotics of the allele frequency
spectrum associated with the Bolthausen-Sznitman
coalescent, with Anne-Laure Basdevant, Electronic
Journal of Probability 13 (2008), Paper no. 17,
[.pdf, arXiv 0706.2808, Oberwolfach report]
- Fragmenting random permutations,
with James Martin and Dario Spanò,
Communications in Probability 13 (2008), Paper no. 44, pp.461-474.
- Behavior near the extinction time in
self-similar fragmentations I: The stable case, with
Bénédicte Haas, Annales de l'Institut
Henri Poincaré (Probabilités et
Statistiques) 46, 2 (2010), pp.338-368. (AIHP prized paper)
- Critical random graphs: limiting
constructions and distributional properties, with
Louigi Addario-Berry and Nicolas Broutin, Electronic Journal of Probability 15 (2010), Paper no. 25, pp.741-775.
[.pdf, arXiv 0908.3629]
- Quantum Heisenberg models and their probabilistic representations, with Daniel Ueltschi and Peter Windridge, Entropy and the Quantum II, Contemporary Mathematics 552 (2011), pp.177-224.
Peter Windridge's simulation of Toth's random stirring model]
- The continuum limit of critical random
graphs, with Louigi Addario-Berry and Nicolas
Theory and Related Fields 152, 3-4 (2012), pp.367-406.
[.pdf, arXiv 0903.4730]
- The scaling limit of the minimum spanning
tree of the complete graph, with Louigi
Addario-Berry, Nicolas Broutin and Grégory Miermont
- Behavior near the extinction time
in self-similar fragmentations II: Finite dislocation
measures, with Bénédicte Haas (2013).
- A line-breaking construction of the
stable trees, with Bénédicte Haas
- Slides from talks
- Slides from four lectures on random trees, random graphs and
fragmentation processes given at Warwick in April
- Slides and the handout from a lecture course given at the Young European Probabilists' Workshop on ``Probability, Random Trees and Algorithms'', EURANDOM, 8th-12th March 2010.
- Slides from my talk at SPA in
Oaxaca, 19th-24th July 2011.
- Slides from my Graduate
Lecture in the Statistics Department, 7th Mrch 2013.
Broutin, Rui Dong,
Johnson, Grégory Miermont, James
- My Erdős number is 3.
- Postdoc and students
- Simon Griffiths (postdoc, jointly with James Martin and Ben Hambly)
- Dominic Yeo (DPhil student, jointly supervised by James
- Eleonora Kreacic (DPhil student, jointly supervised by James Martin)
Some mathematical links can be found on my maths page
and some non-work links can be found on my personal