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

• Chen, Lung-Chi

• Sakai, Akira

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.

Journal

• Probability Theory and Related Fields

  Probability Theory and Related Fields 145 (3-4), 435-458, 2009-11

  Springer Berlin / Heidelberg

Keywords

• Long-range oriented percolation
• Mean-field critical behavior
• Limit theorem
• Crossover phenomenon
• Lace expansion
• Fractional moments

Details

• CRID: 1050001339001038720
• NII Article ID: 120002513620
• DOI: 10.1007/s00440-008-0174-6
• ISSN: 14322064
• ISSN: 01788051
• HANDLE: 2115/44103
• Web Site: https://link.springer.com/content/pdf/10.1007/s00440-008-0174-6.pdf
• Web Site: https://link.springer.com/article/10.1007/s00440-008-0174-6/fulltext.html
• Web Site: http://link.springer.com/content/pdf/10.1007/s00440-008-0174-6
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN