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|Additional Physical Format:||Printed edition:|
|Material Type:||Document, Internet resource|
|Document Type:||Internet Resource, Computer File|
|All Authors / Contributors:||
A Dembo; T Funaki
|ISBN:||9783540260691 3540260692 9783540315377 3540315373|
|Description:||1 online resource (281 pages) illustrations.|
|Series Title:||Lecture Notes in Mathematics / Ecole d'eté Probabilit. Saint-Flour Ser.|
This volume contains two of the three lecturesnbsp;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 f interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.