Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation
成果类型：
Article
署名作者：
Chen, Lung-Chi; Sakai, Akira
署名单位：
Hokkaido University; Fu Jen Catholic University
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-008-0174-6
发表日期：
2009
页码：
435-458
关键词：
摘要：
We prove that the Fourier transform of the properly scaled normalized two-point function for sufficiently spread-out long-range oriented percolation with index alpha > 0 converges to e(-C)vertical bar k vertical bar(alpha boolean AND 2) for some C is an element of (0, infinity) above the upper- critical dimension d(c) equivalent to 2(alpha boolean AND 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 alpha = 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.