Effects of confinement on the statistics of encounter times: exact analytical results for random walks in a partitioned lattice

We study the effects of temporarily and permanently confining domains on the statistics of first-passage times in finite lattices in one and two dimensions. We present exact results for the mean and variance of the first-passage time between arbitrary sites in the following: (1) a finite one-dimensional lattice partitioned into temporarily confining domains and (2) a finite two-dimensional lattice with reflecting boundaries for a single random walker and an immobile target. In the one-dimensional case, we also present the full first-passage time distribution via numerical inversion of Laplace transforms.

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