Boris Tsirelson, Wendelin Werner, W. Werner

Lectures on Probability Theory and Statistics

Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002
Herausgeber: Picard, Jean

• Broschiertes Buch

Produktbeschreibung

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

• Lecture Notes in Mathematics 1840
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-540-21316-1
• 2004
• Seitenzahl: 212
• Erscheinungstermin: 21. April 2004
• Englisch
• Abmessung: 235mm x 155mm x 12mm
• Gewicht: 322g
• ISBN-13: 9783540213161
• ISBN-10: 3540213163
• Artikelnr.: 12687935

Autorenporträt

Boris Tsirelson, Tel Aviv University, Tel Aviv, Israel / Wendelin Werner, Université Paris-Sud, Orsay, France

Inhaltsangabe

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.