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Lectures on Probability Theory and Statistics

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

  • Authors
  • Boris Tsirelson
  • Wendelin Werner
  • Editors
  • Jean Picard

Part of the Lecture Notes in Mathematics book series (LNM, volume 1840)

Table of contents

  1. Front Matter
    Pages I-VII
  2. Back Matter
    Pages 197-200

About this book

Introduction

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.

Keywords

Probability theory Random variable Schramm-Loewner evolutions Variance classical and nonclassical noises random planar curves scaling limits for random variables and processes

Bibliographic information

  • DOI https://doi.org/10.1007/b96719
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-21316-1
  • Online ISBN 978-3-540-39982-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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