A level line of the Gaussian free field with measure-valued boundary conditions  

作　　者：Titus Lupu Hao Wu 

机构地区：[1]Laboratoire de Probabilités,Statistique et Modélisation,Sorbonne Universitéand UniversitéParis Cité,CNRS,Paris F-75005,France [2]Yau Mathematical Sciences Center,Tsinghua University,Beijing 100084,China

出　　处：《Science China Mathematics》2024年第2期367-404,共38页中国科学（数学）（英文版）

基　　金：supported by the French National Research Agency (ANR) within the Project Marches aléatoires en interaction (MALIN) (Grant No. ANR-16-CE93-0003);supported by Beijing Natural Science Foundation (Grant No. JQ20001)

摘　　要：In this article, we construct samples of Schramm-Loewner-evolution-like curves out of samples ofthe conformal loop ensemble and Poisson point processes of Brownian excursions. We show that the laws of thesecurves depend continuously on the intensity measure of the Brownian excursions. Using such a construction ofcurves, we extend the notion of level lines of the Gaussian free field to the case where the boundary conditionis measure-valued.

关 键 词：Schramm-Loewner evolution conformal loop ensemble Brownian excursion Gaussian free field 

分 类 号：O174.12[理学—数学]