This volume contains two of the three lectures that were given at the 33rd 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.
| ISBN: | 9783540260691 |
| Publication date: | 3rd November 2005 |
| Author: | Ecole dété de probabilités de SaintFlour, Amir Dembo, Tadahisa Funaki |
| Publisher: | Springer an imprint of Springer Berlin Heidelberg |
| Format: | Paperback |
| Pagination: | 281 pages |
| Series: | Lecture Notes in Mathematics |
| Genres: |
Probability and statistics Stochastics Differential calculus and equations Integral calculus and equations Calculus and mathematical analysis |