Peculiarities of random walks with resetting in a one-dimensional chain

Abstract

The main characteristics (stationary probability distribution and mean first passage time, MFPT) of random walks on the nodes of a (semi)infinite chain with resetting are obtained. It is shown that their dependences on the resetting rate frequency r essentially differ from those within the classical continuous diffusion model. The same is true for a finite chain in which the existence of an optimal value r * that minimizes the MFPT becomes critically dependent on the resetting node position. As one of non-standard application of the results, the counter-intuitive effect of enzymatic reaction acceleration by increasing the rate of unproductive dissociation of the enzyme-substrate complex is explained.