2020/07/31 by Manuele Onofri, Gaia Pozzoli, Mattia Radice +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Algebra over a field #Applied mathematics #Diffusion #Diffusion and Search Dynamics #Homogeneous #Logarithm #Mathematical analysis #Mathematics #Physics #Position (finance) #Pure mathematics #Quantum mechanics #Random walk #Statistical Mechanics and Entropy #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/abbed6
published as J. Stat. Mech. 2020, 113201 (2020) · 30 pages, 8 figures
openalex created_date 2020/07/29 · openalex publication_date 2020/11/01 · arxiv created 2020/11/12 · arxiv updated 2020/11/13 · openalex updated_date 2026/08/05
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.