GAUSSIAN FREE FIELD LIGHT CONES AND SLEκ (ρ)

• 成果类型: Article
• 署名作者: Miller, Jason; Sheffield, Scott
• 署名单位: University of Cambridge; Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1331
• 发表日期: 2019
• 页码: 3606-3648
• 关键词: reversibility; Duality

摘要

Let h be an instance of the GFF. Fix kappa is an element of (0, 4) and chi = 2//root kappa - root kappa/2. Recall that an imaginary geometry ray is a flow line of e(i(h/chi+theta)) that looks locally like SEE kappa. The light cone with parameter theta is an element of [0, pi] is the set of points reachable from the origin by a sequence of rays with angles in [-theta/2, theta/2]. It is known that when theta = 0, the light cone looks like SLE kappa, and when = theta = pi looks like the range of an SLE16/kappa counterflow line. We find that when theta is an element of (0, pi) the light cones are either fractal carpets with a dense set of holes or space-filling regions with no holes. We show that every nonspace-filling light cone agrees in law with the range of an SLE kappa (rho) process with rho is an element of ((-2 - kappa/2) boolean OR (kappa/2 - 4), -2). Conversely, the range of any such SLE kappa (rho) process agrees in law with a non-space-filling light cone. As a consequence of our analysis, we obtain the first proof that these SLE kappa(rho) processes are a.s. continuous curves and show that they can be constructed as natural path-valued functions of the GFF.