Equilibrium states of diffusion-limited reactions

Diffusion-limited reactions A+B→inert, with input A,B, or the black reaction (inert→A+B), are studied. I have found that in equilibrium, segregation phenomena can occur below or in two dimensions, with typical size of A-rich and B-rich clusters ξ∼1/$R^{2/2\mathrm{-}d}$ for d<2 and ξ∼exp(1/$R^2$) for d=2, respectively, where R is the A and B input rate or back-reaction rate.