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Schramm–Loewner Evolution

  • Book
  • © 2017

Overview

Authors:
  1. Antti Kemppainen

    1. Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

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Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 24)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Antti Kemppainen
    Pages 1-10

  3. Introduction to Stochastic Calculus

    • Antti Kemppainen
    Pages 11-34

  4. Introduction to Conformal Mappings

    • Antti Kemppainen
    Pages 35-47

  5. Loewner Equation

    • Antti Kemppainen
    Pages 49-67

  6. Schramm–Loewner Evolution

    • Antti Kemppainen
    Pages 69-100

  7. Regularity and Convergence of Random Curves

    • Antti Kemppainen
    Pages 101-141

  8. Back Matter

    Pages 143-145
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Keywords

About this book

This book is a short, but complete, introduction to the Loewner equation and the SLEs, which are a family of random fractal curves, as well as the relevant background in probability and complex analysis. The connection to statistical physics is also developed in the text in an example case. The book is based on a course (with the same title) lectured by the author. First three chapters are devoted to the background material, but at the same time, give the reader a good understanding on the overview on the subject and on some aspects of conformal invariance. The chapter on the Loewner equation develops in detail the connection of growing hulls and the differential equation satisfied by families of conformal maps. The Schramm–Loewner evolutions are defined and their basic properties are studied in the following chapter, and the regularity properties of random curves as well as scaling limits of discrete random curves are investigated in the final chapter. The book is aimed at graduate students or researchers who want to learn the subject fairly quickly.

Authors and Affiliations

  • Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland

    Antti Kemppainen

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