Lectures on probability theory and statistics : Ecole d'eté de probabilités de Saint-Flour XXXII - 2002

Author(s)

• École d'été de probabilités de Saint-Flour
• Tsirelson, Boris
• Werner, Wendelin
• Picard, Jean

Bibliographic Information

Lectures on probability theory and statistics : Ecole d'eté de probabilités de Saint-Flour XXXII - 2002

Boris Tsirelson, Wendelin Werner ; editor, Jean Picard

（Lecture notes in mathematics, 1840）

Springer, c2004

Other Title

Lectures on probability theory and statistics, St. Flour 2001

Note

"Three series of lectures were given at the 32nd Probability Summer School in Saint-Flour (July 7-24, 2002)"--Pref

Includes bibliographical references

Description and Table of Contents

Description

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.

Table of 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.- 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.

by "Nielsen BookData"

Details

• NCID: BA66999524
• ISBN:
  • 3540213163
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Berlin ; Tokyo
• Pages/Volumes: 200 p.
• Size: 24 cm
• Classification:
  • LCC : QA273.A1
  • DC22 : 519.2
• Subject Headings:
  • LCSH : Probabilities -- Congresses
  • LCSH : Mathematical statistics -- Congresses
• Parent Bibliography ID:
  • BA00146586