SLE and alpha-SLE driven by Levy processes

doi:10.1214/07-AOP355

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	SLE and alpha-SLE driven by Levy processes
	Guan, Qing-Yang1 ; Winkel, Matthias 2
刊名	ANNALS OF PROBABILITY
	2008-07-01
卷号	36 期号:4 页码:1221-1266
关键词	stochastic Loewner evolution Levy process alpha-stable process self-similarity hitting times
ISSN号	0091-1798
DOI	10.1214/07-AOP355
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	INST MATHEMATICAL STATISTICS
WOS记录号	WOS:000258551700002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/6258]
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.