Fluctuation statistics in the diffusion-limitedA+B→0 reaction

We study the diffusion-limited reaction A+B{→}0 analytically by means of fluctuation statistics. Here we consider both the case of equal (A₀=B₀) and that of unequal (A₀{B}₀$) numbers of reacting particles. We show that the obtained analytical results are in good agreement with computer simulations, in which we focus on reactions in one and two dimensions. Furthermore, as expected from our analytical development, the simulations for different initial concentrations coincide when properly rescaled.