Probability

Research in probability ranges broadly from modern discrete probability and the theory of algorithms to classical and modern stochastic process theory.
Continuous Stochastic ProcessesJim Pitman has longstanding interests in distributional properties of multi-dimensional Brownian motion, and Yuval Peres has worked on the fine structure of sample paths of Brownian motion. Steve Evans has worked extensively on superprocesses and other measure-valued processes that arise in population biology. Probability in Algorithms and PhylogenyMixing times for finite Markov chains are of interest both in the theory of algorithms and statistical physics, and in Berkeley are studied by David Aldous, Elchanan Mossel, Yuval Peres, and Alistair Sinclair. Phase transitions in hard combinatorial optimisations problems over random data are studied by Yuval Peres and David Aldous. Rigorous study of the much used but ill understood survey propogation algorithm is underway by Elchanan Mossel and Martin Wainwright. Elchanan Mossel also studies information theoretic limits to phylogenetic reconstruction. Steve Evans and Terry Speed have worked on the phylogenetic invariants in tree reconstruction and Steve Evans has also worked on phylogenetic methods in historical linguistics. Infinite Discrete Random StructuresYuval Peres works on a range of topics exemplified by percolation on non-amenable groups, and uniform and minimal spanning forests on groups and lattices. Probabilistic CombinatoricsDavid Aldous and Jim Pitman have worked on size-asymptotics for random combinatorial structures such as trees, graphs, permutations and partitions, as well as irreversible models for coalescence and fragmentation. Probabilistic methodology leads to consideration of continuous limit objects ranging from interval splitting to the continuum random tree.

http://www.stat.berkeley.edu/?id=26#probability

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