Schramm–Loewner Evolution
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...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Cham :
Springer International Publishing : Imprint: Springer,
2017.
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| Σειρά: | SpringerBriefs in Mathematical Physics,
24 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- Introduction
- Iteration of conformal maps
- On stochastic models and connection to statistical physics
- An example: percolation model and Cardy’s formula
- On reading this book
- Introduction to stochastic calculus
- Brownian motion
- Stochastic integration
- Itô’s formula
- Further topics in stochastic calculus
- Conformal invariance of two-dimensional Brownian motion
- Weak convergence of probability measures
- Introduction to conformal mappings
- Harmonic functions
- Conformal maps
- From Area theorem to distortion
- Conformally invariant tools
- Loewner equation
- Conformal maps of the upper half-plane
- Loewner chains
- Loewner equations in D and Sp
- Schramm–Loewner evolution.-Schramm–Loewner evolution and its elementary properties
- Advanced properties of SLE
- Proofs for some of the advanced properties
- Variants of SLE
- Moments of the derivative of the Loewner map of SLE(k)
- Regularity and convergence of random curves
- Continuity properties of the Loewner chains
- Continuity of SLE(k)
- Convergence of interfaces in the site percolation model
- Index.
