Survival probability in one dimension for the A+B->B reaction with hard-core repulsion

We study the effect of hard-core repulsion (known as the bus effect) between B particles on the reaction-diffusion system A + B --> B in the continuous-time random walk model in one dimension with the A particles stationary. We show rigorously that the survival probability of the A particles is asymptotically bounded as C-1 greater than or equal to lim(t-->infinity){[-log S(t)]/t(0.5)} greater than or equal to C-2, where C-1 and C-2 are constants. We also do simulations to confirm our results.