Meanfield behavior of nearestneighbor oriented percolation on the BCC lattice above $8+1$ dimensions
Abstract
In this paper, we consider nearestneighbor oriented percolation with independent Bernoulli bondoccupation probability on the $d$dimensional bodycentered cubic (BCC) lattice $\mathbb{L}^d$ and the set of nonnegative integers $\mathbb{Z}_+$. Thanks to the nice structure of the BCC lattice, we prove that the infrared bound holds on $\mathbb{L}^d\times\mathbb{Z}_+$ in all dimensions $d\geq 9$. As opposed to ordinary percolation, we have to deal with the complex numbers due to asymmetry induced by timeorientation, which makes it hard to estimate the bootstrapping functions in the laceexpansion analysis from above. By investigating the FourierLaplace transform of the randomwalk Green function and the twopoint function, we drive the key properties to obtain the upper bounds and resolve a problematic issue in Nguyen and Yang's bound, which is caused by the fact that the Fourier transform of the randomwalk transition probability can take $1$.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.14211
 Bibcode:
 2021arXiv210614211C
 Keywords:

 Mathematical Physics;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Probability;
 82C43 (Primary) 60K35 (Secondary)
 EPrint:
 36 pages, a lot of figures with TikZ. Delete a reference and change the LaTeX compiler