Sisyphus random walk
Mathematical Physics
2016-09-28 v2 Statistical Mechanics
math.MP
Probability
Abstract
In this paper we consider a particular version of the random walk with restarts: random reset events which bring suddenly the system to the starting value. We analyze its relevant statistical properties like the transition probability and show how an equilibrium state appears. Formulas for the first-passage time, high-water marks and other extreme statistics are also derived: we consider counting problems associated naturally to the system. Finally we indicate feasible generalizations useful for interpreting different physical effects.
Cite
@article{arxiv.1603.09239,
title = {Sisyphus random walk},
author = {Miquel Montero and Javier Villarroel},
journal= {arXiv preprint arXiv:1603.09239},
year = {2016}
}
Comments
10 pages, 7 figures; revised version