Diffusive search for buried targets

Various biophysical processes require a diffusing particle to escape from a large bulk volume through one of several narrow tubes. In this paper, we extend recent estimates of this average escape time by analyzing a more general model of particle diffusion, particle absorption, and domain geometry. A salient feature of our model is that the diffusion coefficient may depend on the spatial location of the particle. Our results predict that the interpretation of the multiplicative noise inherent to any spatially varying diffusion coefficient can strongly affect the average escape time.