The effects of random reset on the dynamics of a non-Markovian random walk

Jafarpour Hamadani, Farhad; Vazini Hekmat, Hamid

doi:10.47176/ijpr.23.1.21612

The effects of random reset on the dynamics of a non-Markovian random walk

Document Type : Original Article

Authors

Farhad Jafarpour Hamadani

Hamid Vazini Hekmat

Physics department, Bu-Ali Sina University, Hamedan, Iran

https://doi.org/10.47176/ijpr.23.1.21612

Abstract

Resetting in stochastic systems is defined in different ways. In this research, a 1D non-Markovian random walk is considered. In this process, the reset changes the dynamics in a way where the random walker, after losing its memory, goes back to a fixed point in space and starts again. In this study we investigate time evolution and also the long-time limit of displacement moments in the presence of resetting. Our calculations in the long-time limit show that the probability distribution function for displacement reaches a steady-state. On the other hand, this distribution never gets to a Gaussian form for any values of the resetting rate. We will show that, in contrast to the case where the process does not undergo resetting, the moments accumulate to finite values. This is confirmed by doing Monte Carlo simulations.

Keywords

resetting

random walk

non-Markovian process

persistent

master equation

Subjects

Complex Systems

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