Defining percolation kinetically on an infinite lattice

Percolation is a structural, geometric concept. We show that it can be defined in a purely kinetic way via a chemical reaction. The A + 12B2 → 0 reaction on a square lattice is chosen. The analysis is done for site percolation on an infinite lattice where a fraction S of sites is active. The approach is via stochastic master equations describing the reaction events. A reactive state is obtained for S > S, where S is the kinetically defined critical occupation probability. For S < S no reaction occurs for t → ∞ on the finite clusters. S is found to be S ≈ 0.63.