Mean-field behavior of Nearest-Neighbor Oriented Percolation on the BCC Lattice Above 8 + 1 Dimensions

In this paper, we consider nearest-neighbor oriented percolation with independent Bernoulli bond-occupation probability on the d-dimensional body-centered cubic (BCC) lattice $${\mathbb {L}^d}$$ and set of non-negative integers $${{\mathbb {Z}}_+}$$ . Thanks to orderly structure BCC lattice, prove that infrared bound holds {L}^d} \times {{\mathbb in all dimensions $$d\ge 9$$ As opposed ordinary percolation, have deal complex numbers due asymmetry induced by time-orientation, which makes it hard bootstrap functions lace-expansion analysis. By investigating Fourier–Laplace transform random-walk Green function two-point function, derive key properties obtain upper bounds resolve a problematic issue Nguyen Yang’s bound. The is caused fact Fourier transition can take value $$-1$$