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Critical behavior and the limit distribution for long-range oriented percolation. I
| Title: | Critical behavior and the limit distribution for long-range oriented percolation. I |
| Authors: | Chen, Lung-Chi Browse this author | | Sakai, Akira Browse this author →KAKEN DB |
| Issue Date: | 2007 |
| Publisher: | Springer |
| Journal Title: | Probability Theory and Related Fields |
| Volume: | 142 |
| Issue: | 1-2 |
| Start Page: | 151 |
| End Page: | 188 |
| Publisher DOI: | 10.1007/s00440-007-0101-2 |
| 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. |
| Rights: | "The original publication is available at www.springerlink.com" |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/44913 |
| 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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