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政大機構典藏 > 理學院 > 應用數學系 > 期刊論文 > Item 140.119/71418

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/71418

Title:	Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation
Authors:	陳隆奇 Chen, Lung-Chi Akira Sakai
Contributors:	應數系
Keywords:	Long-range oriented percolation;Mean-field critical behavior;Limit theorem;Crossover phenomenon;Lace expansion;Fractional moments;60K35;82B27
Date:	2009.10
Issue Date:	2014-11-13 17:22:54 (UTC+8)
Abstract:	We prove that the Fourier transform of the properly scaled normalized two-point function for sufficiently spread-out long-range oriented percolation with index α > 0 converges to e−C\|k\|α∧2 for some C∈(0,∞) above the upper-critical dimension dc≡2(α∧2) . This answers the open question remained in the previous paper (Chen and Sakai in Probab Theory Relat Fields 142:151–188, 2008). Moreover, we show that the constant C exhibits crossover at α = 2, which is a result of interactions among occupied paths. The proof is based on a new method of estimating fractional moments for the spatial variable of the lace-expansion coefficients.
Relation:	Probability Theory and Related Fields, 145, 435-458
Data Type:	article
Appears in Collections:	[應用數學系] 期刊論文

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