Generalized disconnection exponents

• 成果类型: Article
• 署名作者: Qian, Wei
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Universite Paris Saclay
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-01005-5
• 发表日期: 2021
• 页码: 117-164
• 关键词: brownian intersection exponents; conformal restriction; VALUES; reversibility; Duality

摘要

We introduce and compute the generalized disconnection exponents eta(kappa)(beta) which depend on kappa is an element of (0, 4] and another real parameter beta, extending the Brownian disconnection exponents (corresponding to kappa = 8/3) computed by Lawler, Schramm and Werner (Acta Math 187(2):275-308, 2001; Acta Math 189(2):179-201, 2002) [conjectured by Duplantier and Kwon (Phys Rev Lett 61:2514-2517, 1988)]. For kappa is an element of (8/3, 4], the generalized disconnection exponents have a physical interpretation in terms of planar Brownian loop-soups with intensity c is an element of (0, 1], which allows us to obtain the first prediction of the dimension of multiple points on the cluster boundaries of these loop-soups. In particular, according to our prediction, the dimension of double points on the cluster boundaries is strictly positive for c. (0, 1) and equal to zero for the critical intensity c = 1, leading to an interesting open question of whether such points exist for the critical loop-soup. Our definition of the exponents is based on a certain general version of radial restriction measures that we construct and study. As an important tool, we introduce a new family of radial SLEs depending on kappa and two additional parameters mu, nu, that we call radial hypergeometric SLEs. This is a natural but substantial extension of the family of radial SLE kappa(rho)s.