Time-reversal of multiple-force-point chordal SLEκ(ρ_)

IF 1.3 3区 数学 Q2 STATISTICS & PROBABILITY Electronic Journal of Probability Pub Date : 2023-01-01 DOI:10.1214/23-ejp1040
Pu Yu
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引用次数: 1

Abstract

Chordal SLEκ(ρ_) is a natural variant of the chordal SLE curve. It is a family of random non-crossing curves on the upper half plane from 0 to ∞, whose law is influenced by additional force points on R. When there are force points away from the origin, the law of SLEκ(ρ_) is not reversible, unlike the ordinary chordal SLEκ. Zhan (2019) gives an explicit description of the law of the time reversal of SLEκ(ρ_) when all force points lie on the same sides of the origin, and conjectured that a similar result holds in general. We prove his conjecture. Specifically, based on Zhan’s result, using the techniques from the Imaginary Geometry developed by Miller and Sheffield (2013), we show that when κ∈(0,8), the law of the time reversal of non-boundary filling SLEκ(ρ_) process is absolutely continuous with respect to SLEκ(ρˆ_) for some ρˆ_ determined by ρ_, with the Radon-Nikodym derivative being a product of conformal derivatives.
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多力点弦态slek (ρ_)的时间反演
脊索slek (ρ_)是脊索SLE曲线的自然变体。它是上半平面上从0到∞的一组随机的不相交曲线,其规律受r上附加的力点的影响。当有远离原点的力点时,SLEκ(ρ_)的规律不可逆,这与普通的弦性SLEκ不同。Zhan(2019)明确描述了所有力点位于原点同侧时slek (ρ_)的时间反转规律,并推测一般情况下也会有类似的结果。我们证明了他的猜想。具体来说,基于Zhan的结果,使用Miller和Sheffield(2013)开发的虚数几何技术,我们证明了当κ∈(0,8)时,对于由ρ_确定的某些ρ_,非边界填充SLEκ(ρ_)过程的时间反转定律相对于SLEκ(ρ_)是绝对连续的,其中Radon-Nikodym导数是共形导数的乘积。
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来源期刊
Electronic Journal of Probability
Electronic Journal of Probability 数学-统计学与概率论
CiteScore
1.80
自引率
7.10%
发文量
119
审稿时长
4-8 weeks
期刊介绍: The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.
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