CSpace  > 应用数学研究所
SLE and alpha-SLE driven by Levy processes
Guan, Qing-Yang1; Winkel, Matthias2
2008-07-01
发表期刊ANNALS OF PROBABILITY
ISSN0091-1798
卷号36期号:4页码:1221-1266
摘要Stochastic Loewner evolutions (SLE) with a multiple root kappa B of Brownian motion B as driving process are random planar curves (if kappa < 4) or growing compact sets generated by a curve (if kappa > 4). We consider here more general Levy processes as driving processes and obtain evolutions expected to look like random trees or compact sets generated by trees, respectively. We show that when the driving force is of the form root kappa B + theta(1/alpha) S for a symmetric a-stable Levy process S, the cluster has zero or positive Lebesgue measure according to whether kappa <= 4 or kappa > 4. We also give mathematical evidence that a further phase transition at alpha = 1 is attributable to the recurrence/transience dichotomy of the driving Levy process. We introduce a new class of evolutions that we call alpha-SLE. They have alpha-self-similarity properties for alpha-stable Levy driving processes. We show the phase transition at a critical coefficient theta = theta(0)(alpha) analogous to the kappa = 4 phase transition.
关键词stochastic Loewner evolution Levy process alpha-stable process self-similarity hitting times
DOI10.1214/07-AOP355
语种英语
WOS研究方向Mathematics
WOS类目Statistics & Probability
WOS记录号WOS:000258551700002
出版者INST MATHEMATICAL STATISTICS
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/6259
专题应用数学研究所
通讯作者Guan, Qing-Yang
作者单位1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 10080, Peoples R China
2.Univ Oxford, Dept Stat, Oxford OX1 3TG, England
推荐引用方式
GB/T 7714
Guan, Qing-Yang,Winkel, Matthias. SLE and alpha-SLE driven by Levy processes[J]. ANNALS OF PROBABILITY,2008,36(4):1221-1266.
APA Guan, Qing-Yang,&Winkel, Matthias.(2008).SLE and alpha-SLE driven by Levy processes.ANNALS OF PROBABILITY,36(4),1221-1266.
MLA Guan, Qing-Yang,et al."SLE and alpha-SLE driven by Levy processes".ANNALS OF PROBABILITY 36.4(2008):1221-1266.
条目包含的文件
条目无相关文件。
个性服务
推荐该条目
保存到收藏夹
查看访问统计
导出为Endnote文件
谷歌学术
谷歌学术中相似的文章
[Guan, Qing-Yang]的文章
[Winkel, Matthias]的文章
百度学术
百度学术中相似的文章
[Guan, Qing-Yang]的文章
[Winkel, Matthias]的文章
必应学术
必应学术中相似的文章
[Guan, Qing-Yang]的文章
[Winkel, Matthias]的文章
相关权益政策
暂无数据
收藏/分享
所有评论 (0)
暂无评论
 

除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。