Poisson point processes, excursions and stable processes in two-dimensional structures (Q972814)

This is a non-formal survey of some processes and measures, connected with two-dimensional stochastic structures. In this relation there are considered a Brownian motion on the plane, a Poisson process of two-dimensional excursions inside a disk, a point field of self-intersections and a Poisson field of loops of the Brownian motion. A connection these structures with the Ising model on the plane is noted. A common property of these structures is invariance of their distributions with respect to conformal transformations of the plane.