多力点弦态slek (ρ_)的时间反演

IF 1.3 3区 数学 Q2 STATISTICS & PROBABILITY
Pu Yu
{"title":"多力点弦态slek (ρ_)的时间反演","authors":"Pu Yu","doi":"10.1214/23-ejp1040","DOIUrl":null,"url":null,"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.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":"7 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Time-reversal of multiple-force-point chordal SLEκ(ρ_)\",\"authors\":\"Pu Yu\",\"doi\":\"10.1214/23-ejp1040\",\"DOIUrl\":null,\"url\":null,\"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.\",\"PeriodicalId\":50538,\"journal\":{\"name\":\"Electronic Journal of Probability\",\"volume\":\"7 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/23-ejp1040\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/23-ejp1040","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 1

摘要

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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Time-reversal of multiple-force-point chordal SLEκ(ρ_)
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.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信