Continuous time random walks under Markovian resetting

TL;DR

This paper studies how Markovian resetting influences continuous time random walks with power-law distributed waiting times and jump lengths, revealing conditions for stationary states and optimal search strategies.

Contribution

It demonstrates the existence of non-equilibrium stationary states and optimal reset rates depending on power-law exponents, advancing understanding of reset-driven search processes.

Findings

Existence of non-equilibrium stationary states under resetting.

Conditions for an optimal reset rate based on power-law exponents.

Identification of parameters minimizing mean first arrival time.

Abstract

We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the existence of a non-equilibrium stationary state and finite mean first arrival time. However, the existence of an optimum reset rate is conditioned to a specific relationship between the exponents of both power law tails. We also investigate the search efficiency by finding the optimal random walk which minimizes the mean first arrival time in terms of the reset rate, the distance of the initial position to the target and the characteristic transport exponents.