Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials
Manuele Onofri,
Gaia Pozzoli,
Mattia Radice
et al.
Abstract:Gillis model, introduced more than 60 years ago, is a nonhomogeneous 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.
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