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Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation
| Title: | Asymptotic behavior of the gyration radius for long-range self-avoiding walk and long-range oriented percolation |
| Authors: | Chen, Lung-Chi Browse this author | | Sakai, Akira Browse this author →KAKEN DB |
| Keywords: | Long-range random walk | | self-avoiding walk | | oriented percolation | | gyration radius | | lace expansion |
| Issue Date: | 2011 |
| Publisher: | Institute of Mathematical Statistics |
| Journal Title: | The Annals of Probability |
| Volume: | 39 |
| Issue: | 2 |
| Start Page: | 507 |
| End Page: | 548 |
| Publisher DOI: | 10.1214/10-AOP557 |
| Abstract: | We consider random walk and self-avoiding walk whose 1-step distribution is given by D, and oriented percolation whose bond-occupation probability is proportional to D. Suppose that D(x) decays as |x|−d − α with α > 0. For random walk in any dimension d and for self-avoiding walk and critical/subcritical oriented percolation above the common upper-critical dimension dc ≡ 2(α ∧ 2), we prove large-t asymptotics of the gyration radius, which is the average end-to-end distance of random walk/self-avoiding walk of length t or the average spatial size of an oriented percolation cluster at time t. This proves the conjecture for long-range self-avoiding walk in [Ann. Inst. H. Poincaré Probab. Statist. (2010), to appear] and for long-range oriented percolation in [Probab. Theory Related Fields 142 (2008) 151–188] and [Probab. Theory Related Fields 145 (2009) 435–458]. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/44917 |
| 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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