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|Material Type:||Online system or service, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
Amir Dembo; Tadahisa Funaki; Jean Picard; Springer-Verlag.
|Other Titles:||SpringerLINK Lecture Notes in Mathematics Contemporary (1997-present)|
This volume contains two of the three lecturesthat were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembos 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 Funakis course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called\nabla \varphiinterface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.