Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions
نویسندگان
چکیده
منابع مشابه
Critical points for spread - out self - avoiding walk , percolation and the contact process above the upper critical dimensions Remco
We consider self-avoiding walk and percolation in Zd, oriented percolation in Z×Z+, and the contact process in Zd, with pD( · ) being the coupling function whose range is denoted by L < ∞. For percolation, for example, each bond {x, y} is occupied with probability pD(y−x). The above models are known to exhibit a phase transition when the parameter p varies around a model-dependent critical poin...
متن کاملCritical points for spread - out self - avoiding walk , percolation and the contact process above the upper critical dimensions
We consider self-avoiding walk and percolation in Zd, oriented percolation in Z×Z+, and the contact process in Zd, with p D( · ) being the coupling function whose range is denoted by L < ∞. For percolation, for example, each bond {x, y} is occupied with probability p D(y−x). The above models are known to exhibit a phase transition when the parameter p varies around a model-dependent critical po...
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Abstract: We consider the critical spread-out contact process in Zd with d ≥ 1, whose infection range is denoted by L ≥ 1. The two-point function τt(x) is the probability that x ∈ Zd is infected at time t by the infected individual located at the origin o ∈ Zd at time 0. We prove Gaussian behaviour for the two-point function with L ≥ L0 for some finite L0 = L0(d) for d > 4. When d ≤ 4, we also ...
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We prove existence of an asymptotic expansion in the inverse dimension, to all orders, for the connective constant for self-avoiding walks on Z d . For the critical point, de ned to be the reciprocal of the connective constant, the coe cients of the expansion are computed through order d 6 , with a rigorous error bound of order d 7 . Our method for computing terms in the expansion also applies ...
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Abstract We consider the critical spread-out contact process in Z with d ≥ 1, whose infection range is denoted by L ≥ 1. The two-point function τt(x) is the probability that x ∈ Z is infected at time t by the infected individual located at the origin o ∈ Z at time 0. We prove Gaussian behavior for the two-point function with L ≥ L0 for some finite L0 = L0(d) for d > 4. When d ≤ 4, we also perfo...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2005
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-004-0405-4