Lectures on probability theory and statistics : Ecole d'Eté de probabilités de Saint-Flour XXXII-2002 / Boris Tsirelson, Wendelin Werner ; editor, Jean Picard.
Contributor(s): Tsirelson, Boris | Werner, WendelinMaterial type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 1840.Publisher: Berlin ; New York : Springer-Verlag, ©2004Edition: 1. AuflDescription: 1 online resource (vii, 200 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540399827; 3540399828Subject(s): Probabilities -- Congresses | Mathematical statistics -- Congresses | Statistics -- Congresses | Mathematical statistics | Probabilities | Statistics | Waarschijnlijkheidstheorie | StatistiekGenre/Form: Electronic books. | Conference papers and proceedings. Additional physical formats: Print version:: Lectures on probability theory and statistics.DDC classification: 519.2 LOC classification: QA3 | .L28 no.1840Online resources: Click here to access online
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Includes bibliographical references and index.
pt. l. Scaling limit, noise, stability / Boris Tsirelson -- pt. 2. Random planar curves and Schramm-Loewner evolutions / Wendelin Werner.
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.