has characteristic spatial description progression with adaptive time step exact solution first-passage Monte Carlo algorithm 2011-05-05 http://identifiers.org/doi/10.1103/PhysRevLett.97.230602 AED DKMC AED diffusion kinetic Monte Carlo method AZ We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations. The new algorithm is exact, extremely efficient, and applicable to many important physical situations in arbitrary integer dimensions. asynchronous event-driven diffusion Monte Carlo Monte Carlo method