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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92802完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林偉傑 | zh_TW |
| dc.contributor.advisor | Wai-Kit Lam | en |
| dc.contributor.author | 周子涵 | zh_TW |
| dc.contributor.author | Tzu-Han Chou | en |
| dc.date.accessioned | 2024-07-01T16:10:40Z | - |
| dc.date.available | 2024-07-02 | - |
| dc.date.copyright | 2024-07-01 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-06-06 | - |
| dc.identifier.citation | [1] Michael Aizenman and David J. Barsky. Sharpness of the phase transition in percolation models. Comm. Math. Phys., 108(3):489–526, 1987.
[2] Antonio Auffinger, Michael Damron, and Jack Hanson. 50 years of first-passage percolation, volume 68. American Mathematical Soc., 2017. [3] Antonio Auffinger and Si Tang. On the time constant of high dimensional first passage percolation. Electron. J. Probab., 21:Paper No. 24, 23, 2016. [4] Raphaël Cerf and Marie Théret. Weak shape theorem in first passage percolation with infinite passage times. Ann. Inst. Henri Poincaré Probab. Stat., 52(3):1351–1381, 2016. [5] J Theodore Cox and Richard Durrett. Some limit theorems for percolation processes with necessary and sufficient conditions. The Annals of Probability, pages 583–603, 1981. [6] Michael Damron, Julian Gold, Wai-Kit Lam, and Xiao Shen. On the number and size of holes in the growing ball of first-passage percolation. Transactions of the American Mathematical Society, 377(03):1641–1670, 2024. [7] Richard Durrett. Oriented percolation in two dimensions. Ann. Probab., 12(4):999–1040, 1984. [8] G. Grimmett. Percolation. Springer, Berlin, 1999. [9] Olle Häggström and Ronald Meester. Asymptotic shapes for stationary first passage percolation. Ann. Probab., 23(4):1511–1522, 1995. [10] J. M. Hammersley. Percolation processes: Lower bounds for the critical probability. Ann. Math. Statist., 28:790–795, 1957. [11] Antonin Jacquet. Geodesics cross any pattern in first-passage percolation without any moment assumption and with possibly infinite passage times. arXiv preprint arXiv:2310.04091, 2023. [12] AntoninJacquet.Geodesicsinfirst-passagepercolationcrossanypattern.Electronic Journal of Probability, 28:1–64, 2023. [13] Harry Kesten. Aspects of first passage percolation. In École d’été de probabilités de Saint Flour XIV-1984, pages 125–264. Springer, 1986. [14] Harry Kesten. Surfaces with minimal random weights and maximal flows: a higher-dimensional version of first-passage percolation. Illinois J. Math., 31(1):99–166, 1987. [15] Régine Marchand. Strict inequalities for the time constant in first passage percolation. The Annals of Applied Probability, 12(3):1001–1038, 2002. [16] M. V. Menshikov. Coincidence of critical points in percolation problems. Dokl. Akad. Nauk SSSR, 288(6):1308–1311, 1986. [17] Jean-ChristopheMourrat.Lyapunovexponents,shapetheoremsandlargedeviations for the random walk in random potential. ALEA Lat. Am. J. Probab. Math. Stat., 9:165–211, 2012. [18] V.Strassen.Theexistenceofprobabilitymeasureswithgivenmarginals.Ann.Math. Statist., 36:423–439, 1965. [19] J. van den Berg and H. Kesten. Inequalities with applications to percolation and reliability. J. Appl. Probab., 22(3):556–569, 1985. [20] Jacob van den Berg and Harry Kesten. Inequalities for the time constant in first-passage percolation. The Annals of Applied Probability, pages 56–80, 1993. [21] John C Wierman. Weak moment conditions for time coordinates in first-passage percolation models. Journal of Applied Probability, 17(4):968–978, 1980. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92802 | - |
| dc.description.abstract | 判斷一個有關初抵滲流模型的不等式中等號是否不會成立通常是一個具有挑戰性的問題。在這篇論文中，我們首先討論了由van den Berg和Kesten得出的嚴格不等式，該不等式涉及到兩個不同分佈對應的時間常數。然後，我們將證明對於一個具有特定條件的分佈，不同維度之間的時間常數存在嚴格不等式。 | zh_TW |
| dc.description.abstract | Determining whether an inequality in first-passage percolation can be strict is usually a challenging problem. In this thesis, we first discuss the strict inequality obtained by van den Berg and Kesten, which concerns the time constants corresponding to two different distributions. Then, we will prove that for a fixed distribution with a mild condition, there exists a strict inequality for the time constants between different dimensions. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-01T16:10:40Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-01T16:10:40Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Verification Letter from the Oral Examination Committee i
摘要 iii Abstract v Contents vii Chapter 1 Introduction 1 1.1 Some Preliminaries........ 2 1.2 Strict Inequalities in First-Passage Percolation........ 5 1.3 A Strict Inequality for the Time Constants Corresponding to Different Distributions........ 8 1.4 A Strict Inequality for the Time Constants Between Different Dimensions........ 11 1.5 Outline of the Thesis........ 11 Chapter 2 Time Constants with Different Distributions 13 2.1 Some Preliminaries........ 14 2.2 Proof of Theorem 1.6........ 18 2.3 Proof of Lemma 2.6: A Resampling Argument........ 23 2.3.1 Exponential Decay of Probability That the Passage Time Gets Close to the Minimum Time........ 23 2.3.2 Proof of Lemma 2.6........ 28 Chapter 3 Time Constants in Different Dimensions 41 3.1 Patterns........ 42 3.2 Proof of Theorem 1.8........ 44 References 51 | - |
| dc.language.iso | en | - |
| dc.subject | 初抵滲流模型 | zh_TW |
| dc.subject | 時間常數 | zh_TW |
| dc.subject | first-passage percolation | en |
| dc.subject | time constant | en |
| dc.title | 探討初抵滲流模型中有關時間常數的嚴格不等式 | zh_TW |
| dc.title | On Strict Inequalities for the Time Constants in First-Passage Percolation | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 李志煌;陳隆奇 | zh_TW |
| dc.contributor.oralexamcommittee | Jhih-Huang Li;Lung-Chi Chen | en |
| dc.subject.keyword | 初抵滲流模型,時間常數, | zh_TW |
| dc.subject.keyword | first-passage percolation,time constant, | en |
| dc.relation.page | 53 | - |
| dc.identifier.doi | 10.6342/NTU202401095 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-06-07 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| 顯示於系所單位： | 數學系 | |
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