Lectures on Probability Theory and Statistics

Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002

École d'Été de Probabilités de Saint-Flour Band 1840

Boris Tsirelson, Wendelin Werner

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Beschreibung


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.

Produktdetails

Einband Taschenbuch
Herausgeber Jean Picard
Seitenzahl 200
Erscheinungsdatum 21.04.2004
Sprache Englisch
ISBN 978-3-540-21316-1
Verlag Springer Berlin
Maße (L/B/H) 23.5/15.5/1.1 cm
Gewicht 670 g
Auflage 2004

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  • Preface.- Part I: Boris Tsirelson: Scaling Limit, Noise, Stability.- Introduction.- A First Look.- Abstract Nonsense of the Scaling Limit.- Scaling Limit and Independence.- Example: The Noise Made by a Poison Snake.- Stability.- Generalizing Wiener Chaos.- Example: The Brownian Web as a Black Noise.- Miscellany.- References.- Index.- Part II: Wendelin Werner: Random Planar Curves and Schramm-Loewner Evolutions.- Introduction.- Loewner Chains.- Chordal SLE.- Chordal SLE and Restriction.- SLE and the Brownian Frontier.- Radial SLE.- Some Critical Exponents for SLE.- Brownian Exponents.- SLE, UST and LERW.- SLE and Critical Percolation.- What is Missing.- References.