From CLE ( κ ) to SLE ( κ , ρ ) ’ s
نویسندگان
چکیده
We show how to connect together the loops of a simple Conformal Loop Ensemble (CLE) in order to construct samples of chordal SLEκ processes and their SLEκ(ρ) variants, and we discuss some consequences of this construction.
منابع مشابه
Reversibility of Some Chordal SLE(κ; ρ) Traces
We prove that, for κ ∈ (0, 4) and ρ ≥ (κ − 4)/2, the chordal SLE(κ; ρ) trace started from (0; 0) or (0; 0−) satisfies the reversibility property. And we obtain the equation for the reversal of the chordal SLE(κ; ρ) trace started from (0; b0), where b0 > 0.
متن کاملDuality of Chordal SLE
We prove that the outer boundary of the final hull of some chordal SLE(κ; ~ ρ) process has the same distribution as the image of some chordal SLE(κ; ~ ρ′) trace, where κ > 4 and κ = 16/κ; and the reversal of some SLE(4; ~ ρ) trace has the same distribution as the time-change of some SLE(4; ~ ρ′) trace. And we also study some geometric properties of some chordal SLE(κ; ~ ρ) traces.
متن کاملDuality of Chordal SLE, II
We improve the geometric properties of SLE(κ; ~ ρ) processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for κ ∈ (4, 8), the boundary of a standard chordal SLE(κ) hull stopped on swallowing a fixed x ∈ R \ {0} is the image of some SLE(16/κ; ~ ρ) trace started from a random point. Using this fact together with a similar propositi...
متن کامل2 3 M ay 2 00 5 SLE coordinate changes
The purpose of this note is to describe a framework which unifies radial, chordal and dipolar SLE. When the definition of SLE(κ; ρ) is extended to the setting where the force points can be in the interior of the domain, radial SLE(κ) becomes chordal SLE(κ; ρ), with ρ = κ − 6, and vice versa. We also write down the martingales describing the Radon-Nykodim derivative of SLE(κ; ρ1, . . . , ρn) wit...
متن کاملar X iv : m at h / 05 05 36 8 v 1 [ m at h . PR ] 1 7 M ay 2 00 5 SLE coordinate changes
The purpose of this note is to describe a framework which unifies radial, chordal and dipolar SLE. When the definition of SLE(κ; ρ) is extended to the setting where the force points can be in the interior of the domain, radial SLE(κ) becomes chordal SLE(κ; ρ), with ρ = κ − 6, and vice versa. We also write down the martingales describing the Radon-Nykodim derivative of SLE(κ; ρ1, . . . , ρn) wit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013