Critical behavior and the limit distribution for long-range oriented percolation. II : Spatial correlation

Chen, Lung-Chi; Sakai, Akira

Probability Theory and Related Fields, 2009, 145(3-4), 435-458

Permalink : https://hdl.handle.net/2115/44103

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アクセス権	open access
URI	https://hdl.handle.net/2115/44103
タイトル	Critical behavior and the limit distribution for long-range oriented percolation. II : Spatial correlation
著者	著者名 Chen, Lung-Chi
著者	e-Rad_Researcher 50506996 著者名 Sakai, Akira
言語	英語
キーワード	Long-range oriented percolation
	Mean-field critical behavior
	Limit theorem
	Crossover phenomenon
	Lace expansion
	Fractional moments
発行日	2009-11
出版者	Springer Berlin / Heidelberg
収録物名	Probability Theory and Related Fields
巻(号)	145(3-4)
ページ	435-458
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
権利情報	The original publication is available at www.springerlink.com
PISSN	0178-8051
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1007/s00440-008-0174-6