政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/80555

English | 正體中文 | 简体中文 | Post-Print筆數 : 27 | Items with full text/Total items : 111300/142216 (78%)
Visitors : 48327747 Online Users : 749

RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.

Home ‧ Login ‧ Upload ‧ Help ‧ About ‧ Administer

政大典藏 > College of Science > Department of Mathematical Sciences > Periodical Articles > Item 140.119/80555

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/80555

Title:	CRITICAL TWO-POINT FUNCTIONS FOR LONG-RANGE STATISTICAL-MECHANICAL MODELS IN HIGH DIMENSIONS
Authors:	陳隆奇 Chen, Lung-Chi Sakai, Akira
Contributors:	應數系
Date:	2015-02
Issue Date:	2016-01-13 16:23:13 (UTC+8)
Abstract:	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.
Relation:	The Annals of Probability, 43(2), 639-681.
Data Type:	article
DOI link:	http://dx.doi.org/10.1214/13-AOP843
DOI:	10.1214/13-AOP843
Appears in Collections:	[Department of Mathematical Sciences] Periodical Articles

Files in This Item:

File	Description	Size	Format
639681.pdf		391Kb	Adobe PDF2	769	View/Open

社群 sharing

著作權政策宣告 Copyright Announcement

1.本網站之數位內容為國立政治大學所收錄之機構典藏，無償提供學術研究與公眾教育等公益性使用，惟仍請適度，合理使用本網站之內容，以尊重著作權人之權益。商業上之利用，則請先取得著作權人之授權。
The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

2.本網站之製作，已盡力防止侵害著作權人之權益，如仍發現本網站之數位內容有侵害著作權人權益情事者，請權利人通知本網站維護人員(nccur@nccu.edu.tw)，維護人員將立即採取移除該數位著作等補救措施。
NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.

Loading...