The survival probability for critical spread-out oriented percolation above 4 + 1 dimensions. I. Induction
نویسندگان
چکیده
منابع مشابه
The survival probability for critical spread-out oriented percolation above 4 + 1 dimensions. I. Induction
We consider critical spread-out oriented percolation above 4+1 dimensions. Our main result is that the extinction probability at time n (i.e., the probability for the origin to be connected to the hyperplane at time n but not to the hyperplane at time n + 1) decays like 1/Bn2 as n →∞, where B is a finite positive constant. This in turn implies that the survival probability at time n (i.e., the ...
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We derive a lace expansion for the survival probability for critical spread-out oriented percolation above 4+1 dimensions, i.e., the probability θn that the origin is connected to the hyperplane at time n, at the critical threshold pc. Our lace expansion leads to a nonlinear recursion relation for θn, with coefficients that we bound via diagrammatic estimates. This lace expansion is for point-t...
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We construct the incipient infinite cluster measure (IIC) for sufficiently spread-out oriented percolation on Zd × Z+, for d + 1 > 4 + 1. We consider two different constructions. For the first construction, we define Pn(E) by taking the probability of the intersection of an event E with the event that the origin is connected to (x, n) ∈ Z×Z+, summing this probability over x ∈ Zd, and normalisin...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2006
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-006-0028-z