Description
In this talk, I review recent advances on the encounter-based approach to diffusion-controlled reactions. This approach relies on the stochastic differential equation for reflected Brownian motion inside a confining domain and employs the joint probability density for the position and the boundary local time of the diffusing particle. The latter characterizes diffusive encounters of the particle with the boundary and thus allows one to incorporate various surface reaction mechanisms, far beyond the conventional one described by Robin boundary condition. I discuss the advantages and versatile applications of the encounter-based approach, including reactions with non-Markovian binding/unbinding kinetics, the resource depletion problem, and the escape