Lectures on Probability Theory and Statistics
Subtitle: Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002 (Lecture Notes in Mathematics)
Contributors: Jean Picard (Editor)
Edition: 1 edition
Publisher: Springer
Published: June 14, 2004
Language: eng
Format: Paperback
Number of pages: 200
ISBN-13: 9783540213161
Subjects: Probability & statistics; Mathematics; Science/Mathematics; Computer Science; Physics; Probability & Statistics - General; 60-1, 60Gxx, 60J65, 60K35, 82B20, 82B27, 82B41; Mathematics / Statistics; Schramm-Loewner evolutions; classical and nonclassical noises; random planar curves; scaling limits for random variables and processes; General
Description: 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). Boris 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. Two examples are examined (noise made by a Poisson snake, the Brownian web). A new framework for the scaling limit is proposed, as well as old and new results about noises, stability, and spectral measures. Wendelin 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.