Abstract
In this paper, we consider the spread-out oriented bond percolation models inZ d ×Z withd>4 and the nearest-neighbor oriented bond percolation model in sufficiently high dimensions. Let η n ,n=1, 2, ..., be the random measures defined onR d by
The mean of η n , denoted by\(\bar \eta _n \), is the measure defined by
We use the lace expansion method to show that the sequence of probability measures\([\bar \eta _n (R^d )]^{ - 1} \bar \eta _n \) converges weakly to a Gaussian limit asn→∞ for everyp in the subcritical regime as well as the critical regime of these percolation models. Also we show that for these models the parallel correlation length\(\xi (p)~|p_c - p|^{ - 1} \) asp⇆pc
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Nguyen, B.G., Yang, WS. Gaussian limit for critical oriented percolation in high dimensions. J Stat Phys 78, 841–876 (1995). https://doi.org/10.1007/BF02183691
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DOI: https://doi.org/10.1007/BF02183691