Thick points of the gaussian free field
文献类型：期刊论文
| 作者 | Hu, Xiaoyu1; Miller, Jason2; Peres, Yuval3 |
| 刊名 | Annals of probability
 |
| 出版日期 | 2010-03-01 |
| 卷号 | 38期号:2页码:896-926 |
| ISSN号 | 0091-1798 |
| 关键词 | Gaussian free field Thick points Extremal points Hausdorff dimension Fractal Conformal invariance |
| DOI | 10.1214/09-aop498 |
| 通讯作者 | Hu, xiaoyu(xyhu@gucas.ac.cn) |
| 英文摘要 | Let u subset of c be a bounded domain with smooth boundary and let f be an instance of the continuum gaussian free field on u with respect to the dirichlet inner product integral(u) del f(x).del g(x)dx. the set t (a; u) of a-thick points of f consists of those z is an element of u such that the average of f on a disk of radius r centered at z has growth root a/pi log 1/r as r -> 0. we show that for each 0 <= a <= 2 the hausdorff dimension of t (a; u) is almost surely 2 - a, that nu(2-a)(t (a; u)) = infinity when 0 < a <= 2 and nu(2)(t(0; u)) = nu(2)(u) almost surely, where nu(alpha) is the hausdorff-alpha measure, and that t(a; u) is almost surely empty when a > 2. furthermore, we prove that t(a; u) is invariant under conformal transformations in an appropriate sense. the notion of a thick point is connected to the liouville quantum gravity measure with parameter gamma given formally by gamma(dz) = e(root 2 pi gamma f(z)) dz considered by duplantier and sheffield. |
| WOS关键词 | ENTROPIC REPULSION ; BROWNIAN-MOTION |
| WOS研究方向 | Mathematics |
| WOS类目 | Statistics & Probability |
| 语种 | 英语 |
| 出版者 | INST MATHEMATICAL STATISTICS |
| WOS记录号 | WOS:000275938300013 |
| URI标识 | http://www.irgrid.ac.cn/handle/1471x/2409881 |
| 专题 | 中国科学院大学 |
| 通讯作者 | Hu, Xiaoyu |
| 作者单位 | 1.Chinese Acad Sci, Dept Math, Beijing 100049, Peoples R China 2.Stanford Univ, Dept Math, Stanford, CA 94305 USA 3.Microsoft Res, Theory Grp, Redmond, WA 98052 USA |
| 推荐引用方式 GB/T 7714 | Hu, Xiaoyu,Miller, Jason,Peres, Yuval. Thick points of the gaussian free field[J]. Annals of probability,2010,38(2):896-926. |
| APA | Hu, Xiaoyu,Miller, Jason,&Peres, Yuval.(2010).Thick points of the gaussian free field.Annals of probability,38(2),896-926. |
| MLA | Hu, Xiaoyu,et al."Thick points of the gaussian free field".Annals of probability 38.2(2010):896-926. |
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来源：中国科学院大学
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