Professor Matthias Winkel

Associate Professor of Probability

Bio

I studied in Münster and Manchester before doing my Ph.D. at the University of Paris 6 (now Sorbonne Université) under the supervision of Jean Bertoin. After a one-year pre- and post-doctoral stay in Aarhus working with Ole Barndorff-Nielsen, I joined the Department of Statistics at Oxford in April 2002.

Research Interests

  • Discrete and continuum random trees and forests, branching processes, superprocesses, tree-valued random processes

  • Exchangeability, random partitions, compositions, random hierarchies, interval partitions

  • Lévy processes, subordinators, time changes

Publications

Rembart, F. and Winkel, M. (2023) “A binary embedding of the stable line-breaking construction”, Stochastic Processes and their Applications, 163, pp. 424–472.
Shi, Q. and Winkel, M. (2023) “Two-sided immigration, emigration and symmetry properties of self-similar interval partition evolutions”, ALEA : Latin American Journal of Probability and Mathematical Statistics, 20, pp. 665–696.
Forman, N., Rizzolo, D., Shi, Q. and Winkel, M. (2023) “Diffusions on a space of interval partitions: the two-parameter model”, Electronic Journal of Probability, 28, pp. 1–46.
Forman, N., Rizzolo, D., Shi, Q. and Winkel, M. (2023) “Diffusions on a space of interval partitions: the two-parameter model”, ELECTRONIC JOURNAL OF PROBABILITY, 28, pp. 1–46.
Shi, Q. and Winkel, M. (2023) “Two-sided immigration, emigration and symmetry prop- erties of self-similar interval partition evolutions”, ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 20, pp. 665–696.
Forman, N., Pal, S., Rizzolo, D. and Winkel, M. (2022) “Ranked masses in two-parameter Fleming-Viot diffusions”, Transactions of the American Mathematical Society, 376, pp. 1089–1111.
Forman, N., Rizzolo, D., Shi, Q. and Winkel, M. (2022) “A two-parameter family of measure-valued diffusions with Poisson–Dirichlet stationary distributions”, Annals of Applied Probability, 32(3), pp. 2211–2253.
Rogers, D. and Winkel, M. (2021) “A Ray-Knight representation of up-down Chinese restaurants”, Bernoulli, 28(1), pp. 689–712.
Rogers, D. and Winkel, M. (2021) “A Ray–Knight representation of up-down Chinese restaurants”, Bernoulli, 28(1), pp. 689–712.
Forman, N., Pal, S., Rizzolo, D. and Winkel, M. (2021) “Diffusions on a space of interval partitions: Poisson-Dirichlet stationary distributions”, Annals of Probability, 49(2), pp. 793–831.

Contact Details

College affiliation: Supernumerary Fellow at Brasenose College

Email: winkel@stats.ox.ac.uk

Office: 3.12

Web: www.stats.ox.ac.uk/~winkel

Research Groups

Probability

Graduate Students

David Geldbach

Matthew Buckland

Gabriel Flath