Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials
Statistical Mechanics
2020-11-13 v2
Abstract
Gillis model, introduced more than 60 years ago, is a non-homogeneous random walk with a position dependent drift. Though parsimoniously cited both in the physical and mathematical literature, it provides one of the very few examples of a stochastic system allowing for a number of exact result, although lacking translational invariance. We present old and novel results for such model, which moreover we show represents a discrete version of a diffusive particle in the presence of a logarithmic potential.
Cite
@article{arxiv.2007.12040,
title = {Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials},
author = {Manuele Onofri and Gaia Pozzoli and Mattia Radice and Roberto Artuso},
journal= {arXiv preprint arXiv:2007.12040},
year = {2020}
}
Comments
30 pages, 8 figures