Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials

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.

arXiv comment30 pages, 8 figures

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Cited by in corpus (10)

• Number of distinct sites visited by a resetting random walker
• Time to reach the maximum for a stationary stochastic process
• Anomalous Diffusion: Fractional Brownian Motion vs. Fractional Ito Motion
• First-passage functionals of Brownian motion in logarithmic potentials and heterogeneous diffusion
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