Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials. (9th November 2020)

• Record Type: Journal Article
• Authors: Onofri, Manuele; Pozzoli, Gaia; Radice, Mattia; Artuso, Roberto
• Is Part Of: Journal of statistical mechanics. (2020:Nov.)
• Publication Date: 2020-11-09
• Subjects: extreme value statistics -- transport properties -- diffusion; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/abbed6
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: The Gillis model, introduced more than 60 years ago, is a non-homogeneous random walk with a position-dependent drift. Though parsimoniously cited both in physical and mathematical literature, it provides one of the very few examples of a stochastic system allowing for a number of exact results, although lacking translational invariance. We present old and novel results for this model, which moreover we show represents a discrete version of a diffusive particle in the presence of a logarithmic potential.