Lectures on Probability Theory and Statistics : Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002 / by Boris Tsirelson, Wendelin Werner ; edited by Jean Picard.

Format:

Book

Author/Creator:

Tsirelson, Boris, author.

Werner, Wendelin, 1968- author.

Contributor:

Picard, Jean, editor.

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1840.

Lecture Notes in Mathematics, 0075-8434 ; 1840

Language:

English

Subjects (All):

Distribution (Probability theory).

Statistical physics.

Probability Theory and Stochastic Processes.

Complex Systems.

Statistical Physics and Dynamical Systems.

Local Subjects:

Probability Theory and Stochastic Processes.

Complex Systems.

Statistical Physics and Dynamical Systems.

Physical Description:

1 online resource (VIII, 200 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004.

System Details:

text file PDF

Summary:

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.

Contents:

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

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.

Other Format:

Printed edition:

ISBN:

9783540399827

Access Restriction:

Restricted for use by site license.