Poisson point processes, excursions and stable processes in two-dimensional structures

Itô's contributions lie at the root of stochastic calculus and of the theory of excursions. These ideas are also very useful in the study of conformally invariant two-dimensional structures, via conformal loop ensembles, excursions of Schramm-Loewner evolutions and Poisson point processes of Brownian loops.Excursions Poisson point processes Brownian motion Bessel processes Schramm-Loewner evolutions Conformal loop ensembles Loop soups