Probability
Our probability research group has been renowned since the 1950s, having included major 20th century figures such as David Blackwell, David Freedman, and Michel Loeve. As well as its historic connection with statistics, in the 21st century probability has much extended its role as a key bridge between theoretical and applied mathematics.
Current faculty research interests include the theory of algorithms, phylogenetic trees, continuous and discrete statistical physics models, combinatorial mathematics, continuum limits of discrete random structures, and distributional properties of (mathematical) Brownian motion.
The majority of this research is collaborative with researchers from other areas of the mathematical sciences, across a broad theory - applied spectrum.
Researchers
analysis of algorithms, applied probability, complex networks, entropy, mathematical probability, phylogenetic trees, random networks, spatial networks, popularization of probability
large random combinatorial structures, random matrices, superprocesses & other measure-valued processes, probability on algebraic structures -particularly local fields, applications of stochastic processes to biodemography, mathematical…
models of percolation, phase transitions in statistical mechanics, mixing time of Markov chains, random walk on graphs, counting problems in non-linear sparse settings
Integrable probability, random matrices, asymptotic representation theory
statistical mechanics, studied rigorously via modern techniques from mathematical probability
statistics, mathematics, probability theory, combinatorics independent random variables, iterated logarithm, tail probabilities, functions of sums
fragmentation, statistics, mathematics, Brownian motion, distribution theory, path transformations, stochastic processes, local time, excursions, random trees, random partitions, processes of coalescence
algorithms, applied probability, statistics, random walks, Markov chains, computational applications of randomness, Markov chain Monte Carlo, statistical physics, combinatorial optimization
Stochastic Processes, Hierarchical Bayesian Inference, Random Graph Theory, Multi-Agent Training, Computational Biology, Solution Continuation, Optimization
mathematics, combinatorics, computational algebraic geometry
Mathematical Statistics, Applied Probability, and Statistical Learning Theory