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We briefly review the principles, mathematical bases, numerical shortcuts andapplications of fast random walk (FRW) algorithms. This Monte Carlo techniqueallows one to simulate individual trajectories of diffusing particles in orderto study various probabilistic characteristics (harmonic measure, firstpassage/exit time distribution, reaction rates, search times and strategies,etc.) and to solve the related partial differential equations. The adaptivecharacter and flexibility of FRWs make them particularly efficient forsimulating diffusive processes in porous, multiscale, heterogeneous, disorderedor irregularly-shaped media.

Efficient Monte Carlo methods for simulating diffusion-reaction processes in complex systems