Critical site percolation in high dimension
arXiv:1911.04159 · doi:10.1007/s10955-020-02607-y
Abstract
We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive several critical exponents that characterize mean-field behavior in high dimensions.
30 pages. Presentation revised