Combinatorial and stochastic inequalities Inequalities that play a key role in the analysis of interacting stochastic systems. All have a very broad range of application. Strong links with combinatorial optimization, information theory, and theoretical computer science. Measure-valued diffusions Stochastic PDE's. Connection to analysis, in particular, non-linear diffusion equations.
Models primarily come from genetics and population dynamics.
Continuum limit of discrete interacting particle systems. Ideas from renormalization theory find fruitful application.