THE TRUNKS OF CLE(4) EXPLORATIONS

• 成果类型: Article
• 署名作者: Lehmkuehler, Matthis
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1895
• 发表日期: 2023
• 页码: 3387-3417
• 关键词: loop

摘要

The family of SLE ⠂mu � 4 (-2) exploration processes with parameter mu e R forms a natural class of conformally invariant ways for discovering the loops of a conformal loop ensemble CLE4. Such an exploration consists of one simple continuous path called the trunk of the exploration that discovers CLE4 loops along the way. The parameter mu appears in the Loewner chain description of the path that traces the trunk and all CLE4 loops encountered by the trunk in chronological order. These explorations can also be interpreted in terms of level lines of a Gaussian free field.It has been shown by Miller, Sheffield and Werner that the trunk of such an exploration is an SLE4(rho, -2 - rho) process for some (unknown) value of rho e (-2, 0). The main result of the present paper is to establish the relation between mu and rho, more specifically to show that mu = -pi cot(pi rho /2).