Resetting random walks in one-dimensional lattices with sinks

Abstract

A standard symmetrical random walk with Poissonian resetting in a chain with terminal sinks is considered. The expressions for probabilities of occupation of chain nodes are obtained for arbitrary values of chain length N, rate k of jumps to adjacent nodes, sink intensities q 0, q N and placements of resetting node n r and starting node n 0. These expressions are used for calculating the dependences of the prime characteristics of the process (unconditional and conditional mean first passage/exit times and splitting probabilities W 0, W N ) on resetting rate r. Among a rich variety of process scenarios, the possibility of inverting the ratio W 0/W N with r growing is of special interest. This provides an effective mechanism of controlling the process outcome.