Lectures on Probability Theory and Statistics (Repost)
Boris Tsirelson, Wendelin Werner, Jean Picard, "Lectures on Probability Theory and Statistics"
2004 | pages: 206 | ISBN: 3540213163 | PDF | 2,3 mb
2004 | pages: 206 | ISBN: 3540213163 | PDF | 2,3 mb
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.
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