论文标题
高斯自由场以及由随机日志驱动的多个SLE
Gaussian free fields coupled with multiple SLEs driven by stochastic log-gases
论文作者
论文摘要
米勒（Miller）和谢菲尔德（Sheffield）将假想表面的概念作为一对等效类别的一对简单地连接的$ \ mathbb {c} $的适当子域，而高斯免费场（GFFS）在共同的等效性下。他们考虑了共弦式Schramm-loewner进化（SLE）给出保形图的情况。在本文中，我们在$ \ mathbb {h} $（上半平面）和$ \ mathbb {o} $（$ \ mathbb {c} $的第一个矫正率）上构建了GFF值的过程，通过将GFF与每个域上的多个SLE耦合。我们证明，如果多个SLE由$ \ \ m athbb {r} $和bru-wishart流程定义的$ \ andbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb = mathbbbbbb，我们证明了$ \ mathbb {h} $和$ \ mathbb {o} $在本地与多个SLE结合使用的gff。我们获得了成对的时间进化域和GFF值的过程。
Miller and Sheffield introduced the notion of an imaginary surface as an equivalence class of pairs of simply connected proper subdomains of $\mathbb{C}$ and Gaussian free fields (GFFs) on them under the conformal equivalence. They considered the situation in which the conformal maps are given by a chordal Schramm--Loewner evolution (SLE). In the present paper, we construct GFF-valued processes on $\mathbb{H}$ (the upper half-plane) and $\mathbb{O}$ (the first orthant of $\mathbb{C}$) by coupling a GFF with a multiple SLE evolving in time on each domain. We prove that a GFF on $\mathbb{H}$ and $\mathbb{O}$ is locally coupled with a multiple SLE if the multiple SLE is driven by the stochastic log-gas called the Dyson model defined on $\mathbb{R}$ and the Bru--Wishart process defined on $\mathbb{R}_+$, respectively. We obtain pairs of time-evolutionary domains and GFF-valued processes.
