Random walks with asymmetric time delays
Statistical Mechanics
2025-05-30 v1 Probability
Populations and Evolution
Abstract
We studied simple random-walk models with asymmetric time delays. Stochastic simulations were performed for hyperbolic-tangent fitness functions and to obtain analytical results we approximated them by step functions. A novel behavior has been observed. Namely, the mean position of a walker depends on time delays. This is a joint effect of both stochasticity and time delays present in the system. We also observed that by shifting appropriately fitness functions we may reverse the effect of time delays - the mean position of the walker changes the sign.
Cite
@article{arxiv.2104.05342,
title = {Random walks with asymmetric time delays},
author = {Kamil Łopuszański and Jacek Miękisz},
journal= {arXiv preprint arXiv:2104.05342},
year = {2025}
}