论文标题
高斯免费领域的讲义
Lecture notes on the Gaussian Free Field
论文作者
论文摘要
连续体中的高斯自由场（GFF）似乎是布朗运动的自然概括，当一个人用多维连续参数取代时间时。这些讲义的目的是描述连续GFF的某些方面及其在晶格上定义的离散对应物的某些方面，目的是为有关该主题的一些最新发展提供温和的独立介绍，例如Continuum GFF，Brownian Loop-Soups和Supportal loop loop clemembles cle（4）。 这是第一作者为EthZürich的研究生课程撰写的注释的更新和扩展的版本。这些音符上半年散布的练习主要源于第二作者为2018年本课程编写的练习表。
The Gaussian Free Field (GFF) in the continuum appears to be the natural generalisation of Brownian motion, when one replaces time by a multidimensional continuous parameter. The goal of these lecture notes is to describe some aspects of the continuum GFF and of its discrete counterpart defined on lattices, with the aim of providing a gentle self-contained introduction to some recent developments on this topic, such as the relation between the continuum GFF, Brownian loop-soups and the Conformal Loop Ensembles CLE(4). This is an updated and expanded version of the notes written by the first author for graduate courses at ETH Zürich. The exercises that are interspersed in the first half of these notes mostly originate from the exercise sheets prepared by the second author for this course in 2018.
