Lectures on Probability Theory and Statistics: Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003 (Lecture Notes in Mathematics / Ecole d'Eté Probabilit.Saint-Flour)

This volume contains two of the three lectures that were given at the 33 rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called \nabla \varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques. Favorite Points, Cover Times and Fractals....Pages 1-101 Stochastic Interface Models....Pages 103-274