Resetting random walks in one-dimensional lattices with sinks

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.

Automated summary

This study examines a standard symmetrical random walk with Poissonian resetting in a chain with terminal sinks. The expressions for probabilities of occupation of chain nodes are derived, and these expressions are used to calculate the main characteristics of the process. It is found that the outcome of the process can be controlled by increasing the resetting rate.