The Probability group's research interests encompass a broad range of topics with surprising interconnections; only a small selection are mentioned here.

**Stochastic Processes and Discrete Random Structures**

Jim Pitman, David Aldous and Steven Evans have longstanding interests in studying limits of finite random structures via some stochastic process construction of a limit structure. This methodology has been applied to random combinatorial structures such as trees, graphs, permutations and partitions, as well as irreversible models for coalescence and fragmentation. Such theory relates to several topics outside mathematics, for instance non-parametric Bayesian priors for clustering analyses and analysis of genealogical trees arising in population genetics.

Jim Pitman and Steven Evans have longstanding interests in properties of Brownian motion and Levy processes, including systems of coalescing particles and convex minorants.

**Mixing Times for Markovian Systems**

Allan Sly studies mixing times for finite spin systems, a class of problems arising from statistical physics and computational complexity. David Aldous studies general "social dynamics" models involving a large finite number of interacting agents.

**Phylogenetic reconstruction**

Elchanan Mossel and Allan Sly have studied information theoretic limits to phylogenetic reconstruction. Steven Evans has applied phylogenetic methods to historical linguistics.

**Other topics**

Elchanan Mossel studies mathematical problems in the context of social choice -- voting, etc -- which have surprising connections with mathematical topics such as discrete analysis and Gaussian geometry.

Numerous faculty based in other departments have interests overlapping with this group's. Alistair Sinclair (Statistics and Computer Science) studies relations between probability and statistical physics on the one hand, and algorithms and computational complexity on the other hand. Fraydoun Rezakhanlou (Mathematics) studies stochastic Hamilton-Jacobi partial differential equations and systems of coalescing particles in three dimensions.