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Critical behavior and the limit distribution for long-range oriented percolation. II : Spatial correlation
| Title: | Critical behavior and the limit distribution for long-range oriented percolation. II : Spatial correlation |
| Authors: | Chen, Lung-Chi Browse this author | | Sakai, Akira Browse this author →KAKEN DB |
| Keywords: | Long-range oriented percolation | | Mean-field critical behavior | | Limit theorem | | Crossover phenomenon | | Lace expansion | | Fractional moments |
| Issue Date: | Nov-2009 |
| Publisher: | Springer Berlin / Heidelberg |
| Journal Title: | Probability Theory and Related Fields |
| Volume: | 145 |
| Issue: | 3-4 |
| Start Page: | 435 |
| End Page: | 458 |
| Publisher DOI: | 10.1007/s00440-008-0174-6 |
| 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. |
| Rights: | The original publication is available at www.springerlink.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/44103 |
| Appears in Collections: | 創成研究機構 (Creative Research Institution) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 坂井 哲
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