| dc.contributor | 應數系 | - |
| dc.creator (作者) | 陳隆奇 | - |
| dc.creator (作者) | Chen, Lung-Chi | - |
| dc.creator (作者) | Sakai, Akira | en_US |
| dc.date (日期) | 2015-02 | - |
| dc.date.accessioned | 13-Jan-2016 16:23:13 (UTC+8) | - |
| dc.date.available | 13-Jan-2016 16:23:13 (UTC+8) | - |
| dc.date.issued (上傳時間) | 13-Jan-2016 16:23:13 (UTC+8) | - |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/80555 | - |
| dc.description.abstract (摘要) | We consider long-range self-avoiding walk, percolation and the Ising model on ZdZd that are defined by power-law decaying pair potentials of the form D(x)≍|x|−d−αD(x)≍|x|−d−α with α>0α>0. The upper-critical dimension dcdc is 2(α∧2)2(α∧2) for self-avoiding walk and the Ising model, and 3(α∧2)3(α∧2) for percolation. Let α≠2α≠2 and assume certain heat-kernel bounds on the nn-step distribution of the underlying random walk. We prove that, for d>dcd>dc (and the spread-out parameter sufficiently large), the critical two-point function Gpc(x)Gpc(x) for each model is asymptotically C|x|α∧2−dC|x|α∧2−d, where the constant C∈(0,∞)C∈(0,∞) is expressed in terms of the model-dependent lace-expansion coefficients and exhibits crossover between α<2α<2 and α>2α>2. We also provide a class of random walks that satisfy those heat-kernel bounds. | - |
| dc.format.extent | 400655 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.relation (關聯) | The Annals of Probability, 43(2), 639-681. | - |
| dc.title (題名) | CRITICAL TWO-POINT FUNCTIONS FOR LONG-RANGE STATISTICAL-MECHANICAL MODELS IN HIGH DIMENSIONS | - |
| dc.type (資料類型) | article | - |
| dc.identifier.doi (DOI) | 10.1214/13-AOP843 | - |
| dc.doi.uri (DOI) | http://dx.doi.org/10.1214/13-AOP843 | - |
