| dc.contributor.advisor | 陳隆奇 | zh_TW |
| dc.contributor.advisor | CHEN, LUNG-CHI | en_US |
| dc.contributor.author (Authors) | 王守朋 | zh_TW |
| dc.contributor.author (Authors) | Wang, Shou-Peng | en_US |
| dc.creator (作者) | 王守朋 | zh_TW |
| dc.creator (作者) | Wang, Shou-Peng | en_US |
| dc.date (日期) | 2020 | en_US |
| dc.date.accessioned | 3-Aug-2020 17:57:38 (UTC+8) | - |
| dc.date.available | 3-Aug-2020 17:57:38 (UTC+8) | - |
| dc.date.issued (上傳時間) | 3-Aug-2020 17:57:38 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0106751002 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/131107 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description (描述) | 106751002 | zh_TW |
| dc.description.abstract (摘要) | self-avoiding walk是線性聚合物的模型。它是機率和統計力學中一個重要而有趣的模型。一些重要問題已經解決(c.f.[5]). 然而，許多重要問題仍未解決，特別是涉及關鍵指數的問題，尤其是遠程模型的關鍵指數。在本文中，我們獲得了對於一個特殊的長域模型，其單步分佈是波松分佈的特殊敏感度模型，其敏感性指數滿足均值場行為，且其值大於上臨界值d(c) = 4 。參數 lambda > lambda(d) 的類型分佈，其中lambda(d)取決於維度。為此，我們選擇一組特殊的 bootstrapping functions，它們類似於[4]，並使用lace expansion分析有關bootstrapping functions的複雜部分。 此外，對於d>4，我們得到lambda(d)的確切值。 | zh_TW |
| dc.description.abstract (摘要) | Self-avoiding walk is a model for linear polymers.It is an important and interesting model in Probability and Statistical mechanics.Some of the important problems had been solved (c.f.[5]). However,many of the important problems remain unsolved, particularly those involving critical exponents, especially the critical exponents for long-range models.In this thesis, we see Lace expansion to obtain that the critical exponent of the susceptibility satisfies the mean-field behavior with the dimensions above the upper critical dimension (d(c) = 4) for a special loge-range model in which each one-step distribution is the Poisson-type distribution with parameter lambda > lambda(d) where lambda(d) depends on the dimensions. To achieve this, we choose a particular set of bootstrapping functions which is similar as [4] and using a notoriously complicated part of the lace expansion analysis. Moreover we get the exactly value of lambda(d) for d > 4. | en_US |
| dc.description.tableofcontents | 1 Introduction 12 Models and Main Results 32.1 Notations and Definitions 32.2 Main results and their proofs 63 The lace expansion for selfavoiding walk 104 Diagrammatic bounds estimate 144.1 Diagrammatic bounds on the lace expansion coefficients 144.2 Diagramatic bounds on the bootstrapping argument 255 Random walk estimate 295.1 The diagrams bound of randomwalk quantities for p = 1295.2 The diagrams bound of randomwalk quantities for p > 1356 Proof of Proposition 2.2.7 2.2.9 406.1 Proof of Proposition 2.2.7 406.2 Proof of Proposition 2.2.8 - 2.2.9 and Lemma 4.1.1 44Appendix A 48Bibliography 50 | zh_TW |
| dc.format.extent | 572132 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0106751002 | en_US |
| dc.subject (關鍵詞) | 雖機漫步 | zh_TW |
| dc.subject (關鍵詞) | self-avoiding walk | en_US |
| dc.title (題名) | 在高維度下受波氏分配自我相斥隨機漫步的均場行為 | zh_TW |
| dc.title (題名) | Mean-field behavior for self-avoiding walks with Poisson interactions in high dimensions | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1] Roland Bauerschmidt, Hugo DuminilCopin,Jesse Goodman, and Gordon Slade. Lectureson selfavoidingwalks, 2012.[2] David Brydges and Thomas Spencer. Selfavoidingwalk in 5 or more dimensions.Communications in Mathematical Physics, 97(1):125–148, Mar 1985.[3] LungChiChen and Akira Sakai. Critical twopointfunction for longrangemodelswith powerlawcouplings: The marginal case for $${d\\ge d_{\\rm c}}$$d≥dc.Communications in Mathematical Physics, 372(2):543–572, 2019.[4] Satoshi Handa, Yoshinori Kamijima, and Akira Sakai. A survey on the lace expansionfor the nearestneighbormodels on the bcc lattice. To appear in Taiwanese Journal ofMathematics, 2019.[5] Takashi Hara and Gordon Slade. Selfavoidingwalk in five or more dimensions. i. thecritical behaviour. Comm. Math. Phys., 147(1):101–136, 1992.[6] Takashi Hara, Remco van der Hofstad, and Gordon Slade. Critical twopointfunctions andthe lace expansion for spreadouthighdimensionalpercolation and related models. Ann.Probab., 31(1):349–408, 01 2003.[7] Markus Heydenreich, Remco van der Hofstad, and Akira Sakai. Meanfieldbehaviorfor longandfinite range ising model, percolation and selfavoidingwalk. Journal ofStatistical Physics, 132(6):1001–1049, 2008.[8] N. Madras and G. Slade. The SelfAvoidingWalk. Probability and Its Applications.Birkhäuser Boston, 1996.[9] Yuri Mejia Miranda and Gordon Slade. The growth constants of lattice trees and latticeanimals in high dimensions, 2011.[10] A Sakai. Lace expansion for the Ising model. Technical Report mathph/0510093, Oct2005.[11] Akira Sakai. Meanfieldcritical behavior for the contact process. Journal of StatisticalPhysics, 104(1):111–143, Jul 2001.[12] Gordon Slade. The lace expansion and its applications, 2005.[13] Remco van der Hofstad, Frank den Hollander, and Gordon Slade. The survival probabilityfor critical spreadoutoriented percolation above 4+1 dimensions. ii. expansion. Annalesde l’Institut Henri Poincare (B) Probability and Statistics, 43(5):509 – 570, 2007.[14] Doron Zeilberger. The abstract lace expansion, 1998. | zh_TW |
| dc.identifier.doi (DOI) | 10.6814/NCCU202000775 | en_US |
