由随机对数气体驱动的多个SLE耦合的高斯自由场
概率论
2021-12-10 v7 统计力学
数学物理
math.MP
摘要
Miller与Sheffield引入了虚曲面的概念，作为的单纯连通真子域及其上的高斯自由场（GFF）在共形等价下的配对等价类。他们考虑了共形映射由弦状Schramm--Loewner演化（SLE）给出的情况。在本文中，我们通过将GFF与在每个域上随时间演化的多个SLE耦合，在（上半平面）和（的第一卦限）上构造GFF值过程。我们证明，若多个SLE分别由定义在上的Dyson模型和定义在上的Bru--Wishart过程这一随机对数气体驱动，则与上的GFF与多个SLE局部耦合。我们获得了时间演化域与GFF值过程的配对。
引用
@article{arxiv.2001.03079,
title = {Gaussian free fields coupled with multiple SLEs driven by stochastic log-gases},
author = {Makoto Katori and Shinji Koshida},
journal= {arXiv preprint arXiv:2001.03079},
year = {2021}
}
备注
v7: LaTex, 21 pages, no figure. This manuscript was prepared for the proceeding of the workshop of the 12th Mathematical Society of Japan, Seasonal Institute (MSJ-SI), `Stochastic Analysis, Random Fields and Integrable Probability', held at Kyushu University, Fukuoka, Japan, July 31--August 9, 2019. The proceeding will be published in Advanced Studies in Pure Mathematics 87, 2021