Probability and Inference Theory
Research on Probability theory is mainly on discrete probability, history-dependent random walks, percolation, dynamic inhomogeneous random graphs, interacting stochastic processes.
Bond percolation on the square, percolation probability 0.52
Possible applications are to the development and analysis of biological neural networks.
Research on Inference theory is on inference for infinite dimensional problems, i.e. problems when the unknown parameter lies in function classes, and on particle filters and state space models. Some research areas are: limit theorems in mathematical statistics, for instance limit distributions for regular and nonregular statistical functionals, order restricted inference, nonparametric methods for dependent data, in particular strong (long range) and weak dependence for stationary processes, nonparametric methods for hidden Markov chains and state space models.
Two estimates and the truth: the Hardy-Littlewood-Polya monotone rearrangement estimate (red), the isotonic regression (blue) and the true density (black).
Possible applications are for instance to density estimation, regression problems and spectral densities.