Research interests: stochastic processes and applications
Main 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
Current Ph.D. students
Matthew Buckland (2020--)
David Geldbach (2021--, joint supervision with Julien Berestycki)
I'm always happy to consider prospective Ph.D. students interested in my main research interests. Feel
free to send me an email if you'd like to find out more about what's behind
these topics. Briefly, my aim is to follow a probabilistic approach sometimes
starting from heuristic arguments, but some advanced probability theory and
analytical tools are required to then establish results rigorously. This is
not meant to sound like a hidden list of prerequisites but you should expect to
spend a good proportion of your time, particularly initially, doing guided
reading of selected parts of the literature to extend your tool kit.
Former Ph.D. students: Almut Veraart (jointly supervised with Neil Shephard, completed in 2007, now at Imperial College London), Di Kuang (jointly supervised with Bent Nielsen, completed in 2008, then at Aon), Bo Chen (completed in 2009, then Goldman Sachs), John Cao (completed in 2011, then Royal Bank of Scotland), Patrick Hoscheit (visiting in 2011, now at INRA), Franz Rembart (completed in 2016, now at Boston Consulting and Columbia University), Dane Rogers (completed in 2020, then medical statistician), Frederik Soerensen (completed in 2021, then BASE life science)
Publications with links to pdf files (preprint versions, where appropriate)
Winkel, M.: Diffusions on a space of interval partitions: construction from Bertoin's BES_0(d), 0\le d\le 1. Electron. Commun. Probab., 25:13pp. (2020)
Rogers, D. and Winkel, M.: A Ray-Knight representation of up-down Chinese restaurants. Bernoulli28(1), 689-712 (2022)
Shi, Q. and Winkel, M.: Up-down ordered Chinese restaurant processes with two-sided immigration, emigration and diffusion limits arXiv:2012.15758 (2020)