Lecture Notes in Mathematics: Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002

Tsirelson, Boris; Picard, Jean; Werner, Wendelin

This is yet another indispensable volume for all probabilists and collectors of the Saint-Flour series, and is also of great interest for mathematical physicists. It contains two of the three lecture courses given at the 32nd Probability Summer School in Saint-Flour (July 7-24, 2002). Tsirelson's lectures introduce the notion of nonclassical noise produced by very nonlinear functions of many independent random variables, for instance singular stochastic flows or oriented percolation. Werner's contribution gives a survey of results on conformal invariance, scaling limits and properties of some two-dimensional random curves. It provides a definition and properties of the Schramm-Loewner evolutions, computations (probabilities, critical exponents), the relation with critical exponents of planar Brownian motions, planar self-avoiding walks, critical percolation, loop-erased random walks and uniform spanning trees.

Details

Published by: Springer

Publication Date: 2004-04-21

Format: Paperback

ISBN-13: 9783540213161

DOI: 10.1007/b96719

Dimensions: 233cm x155cm

Pages: 200