Lectures on probability theory and statistics : Ecole d'eté de probabilités de Saint-Flour XXXII - 2002
著者
書誌事項
Lectures on probability theory and statistics : Ecole d'eté de probabilités de Saint-Flour XXXII - 2002
（Lecture notes in mathematics, 1840）
Springer, c2004
- タイトル別名
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Lectures on probability theory and statistics, St. Flour 2001
大学図書館所蔵 全70件
注記
"Three series of lectures were given at the 32nd Probability Summer School in Saint-Flour (July 7-24, 2002)"--Pref
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
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.
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