INFERRING THE DISTRIBUTION OF INTER-REACTION INTERVALS FOR DIFFUSION-LIMITED REACTIONS ON LATTICES

We study the operator-split method Gillespie-MultiParticle method (GMP) for a diffusion-limited reaction in a finite medium by looking at the detailed distribution of reaction times for a broad range of time scales. The diffusion-limited reaction lies at the lower limits of the applicability of the GMP method. We propose an empirical distribution for the inter-reaction times (duration of the dissociated state) that accounts for the power-law and exponential regimes. The knowledge of this distribution can be used to change the reactive method of GMP and enable it to use coarser discretization, with consequent improvement in performance.