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Title: Critical behavior and the limit distribution for long-range oriented percolation
Authors: 陳隆奇
Chen, Lung-Chi
Akira Sakai
Contributors: 應數系
Date: 2008.09
Issue Date: 2014-11-13 17:22:14 (UTC+8)
Abstract: We consider oriented percolation on Zd×Z+ whose bond-occupation probability is pD( · ), where p is the percolation parameter and D is a probability distribution on Zd . Suppose that D(x) decays as |x|−d−α for some α > 0. We prove that the two-point function obeys an infrared bound which implies that various critical exponents take on their respective mean-field values above the upper-critical dimension dc=2(α∧2) . We also show that, for every k, the Fourier transform of the normalized two-point function at time n, with a proper spatial scaling, has a convergent subsequence to e−c|k|α∧2 for some c > 0.
Relation: Probability Theory and Related Fields, 140, 151-188
Data Type: article
Appears in Collections:[應用數學系] 期刊論文

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