SLE and alpha-SLE driven by Levy processes
文献类型：期刊论文
| 作者 | Guan, Qing-Yang1 ; Winkel, Matthias2
|
| 刊名 | ANNALS OF PROBABILITY
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000258551700002 |
| 出版者 | INST MATHEMATICAL STATISTICS |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
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。