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Schramm–Loewner evolution

Antti Kemppainen

A manuscript, latest version 2017/06/29 

Reference to this book

A.Kemppainen: Schramm-Loewner evolution. (2017)
To appear in the series SpringerBriefs in Mathematical Physics. DOI: 10.1007/978-3-319-65329-7 .

Preface

This is a book manuscript based on my lecture courses on Schramm–Loewner evolutions, lectured in fall 2011 and in spring 2016. It includes additional material on scaling limits of random curves (related to my own research — among others, the article "Random curves, scaling limits and Loewner evolutions").

Due to restrictions in the total number of pages, some amount of material has been extracted from the main text to appendices.

Chapters

The main text (here) (version 2017/06/09)

  1. Introduction
  2. Introduction to stochastic calculus
  3. Introduction to conformal mappings
  4. Loewner equation
  5. Schramm–Loewner evolution
  6. Regularity and convergence of random curves

(you can also check the fall 2011 and spring 2016 lecture notes) 

Appendices

The appendices (here) (updated 2017/06/29)

(See also spring 2016 lecture notes)

  • Supplementary material on probability theory
  • Supplementary material on stochastic calculus
  • Supplementary material on complex analysis
  • Supplementary material on convergence of random curves

Exercises

The exercises (here) (updated 2017/06/29)

(See also spring 2016 problem sheets)

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