Catálogo de publicaciones - libros

In this course we follow recent advances in the study of the fractal nature of certain random sets, emphasizing the methods used to obtain such results. We focus on some of the fine properties of the sample path of the most basic stochastic processes such as simple random walks, Brownian motion, and symmetric stable processes. As we shall see, probability on trees inspires many of our proofs, with trees used to model the relevant correlation structure. Along the way we also mention quite a few challenging open research problems. Among the methods that will be detailed here are

In these notes we try to review developments in the last decade of the theory on stochastic models for interfaces arising in two phase system, mostly on the so-called ⊸φ interface model. We are, in particular, interested in the scaling limits which pass from the microscopic models to macroscopic level. Such limit procedures are formulated as classical limit theorems in probability theory such as the law of large numbers, the central limit theorem and the large deviation principles.