Article Outline

Date: 2015-10-07; view: 484.

1. Introduction

1.1. Historical overview

1.2. Aims of this article

2. Random curves and lattice models

2.1. The Ising and percolation models

2.1.1. Exploration process

2.2. O (n) model

2.3. Potts model

2.4. Coulomb gas methods

2.4.1. Winding angle distribution

2.4.2. N-leg exponent

3. SLE

3.1. The postulates of SLE

3.2. Loewner's equation

3.3. Schramm–Loewner evolution

3.4. Simple properties of SLE

3.4.1. Phases of SLE

3.4.2. SLE duality

3.5. Special values of κ

3.5.1. Locality

3.5.2. Restriction

3.6. Radial SLE and the winding angle

3.6.1. Identification with lattice models

4. Calculating with SLE

4.1. Schramm's formula

4.2. Crossing probability

4.3. Critical exponents from SLE

4.3.1. The fractal dimension of SLE

4.3.2. Crossing exponent

4.3.3. The one-arm exponent

5. Relation to conformal field theory

5.1. Basics of CFT

5.2. Radial quantisation

5.3. Curves and states

5.4. Differential equations

5.4.1. Calogero–Sutherland model

6. Related ideas

6.1. Multiple SLEs

6.2. Other variants of SLE

6.3. Other growth models

Acknowledgements

References