The asymptotic expansion of the critical point shows behavior aligning with powers of d^{-1}, enhancing mathematical understanding.
Analysis reveals how the critical point evolves as dimensions increase, characterizing its dependency on d.
This method utilizes the lace expansion, providing a novel approach to study percolation in high dimensions.
Findings offer implications for theoretical models of percolation, potentially guiding future mathematical explorations.
Abstract
We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on Zᵈ in powers of d^-1 as d. The proof relies heavily on the lace expansion.