随机Loewner演化介绍

An introduction to the stochastic Loewner evolution

本文对随机Loewner演化(stochastic Loewner evolution, SLE)这一新的研究方向做一个综述性的介绍.随机Loewner演化是Oded Schramm于2000年前后创立的曲线上的单参数共形不变测度族理论.它与复分析、共形几何、分形几何和随机分析有非常紧密的联系,特别是在统计物理中有十分重要的应用.

This expository article gives an introduction to the stochastic Loewner evolution(SLE). SLE, introduced by Oded Schramm in around 2000, is a one-parameter family of conformal invariant measures on random curves, and is closely related to complex analysis, conformal geometry, fractal geometry and stochastic analysis,etc., with particularly important applications in statistical physics.