open access

https://hdl.handle.net/2115/44913

Critical behavior and the limit distribution for long-range oriented percolation. I

英語

2007

Springer

Probability Theory and Related Fields

142(1-2)

151-188

We consider oriented percolation on Zd × Z+ whose bond-occupation probability is pD( · ), where p is the percolation parameter and D is a probability distribution on Zd . Suppose that D(x) decays as |x|−d−α for some α > 0. We prove that the two-point function obeys an infrared bound which implies that various critical exponents take on their respective mean-field values above the upper-critical dimension dc = 2(α ∧2).We also show that, for every k, the Fourier transform of the normalized two-point function at time n,with a proper spatial scaling, has a convergent subsequence to e−c|k|α∧2 for some c > 0.

学術雑誌論文

Accepted Manuscript

"The original publication is available at www.springerlink.com"

0178-8051

AA10531847