Random walks with homotopic spatial inhomogeneities

Ignacio S. Gomez, Daniel Rocha de Jesus and Ronaldo Thibes

Physica A: Statistical Mechanics and its Applications, 2025, vol. 676, issue C

Abstract: In this work, we study a generalization of the standard random walk, an homotopic random walk (HRW), using a deformed translation unitary step that arises from a homotopy of the position-dependent masses associated to the Tsallis and Kaniadakis nonextensive statistics. The HRW implies an associated homotopic Fokker–Planck equation (HFPE) provided with a bi-parameterized inhomogeneous diffusion. The trajectories of the HRW exhibit convergence to a position, randomness as well as divergence. The HFPE presents the features: (a) it results an special case of the van Kampen diffusion equation (5) of Ref. [N. G. van Kampen, Z. Phys. B Condensed Matter68, 135 (1987)]; (b) it exhibits a superdiffusion; (c) Tsallis and Kaniadakis deformed FPE are recovered as special cases; (d) a homotopic mixtured diffusion is observed; and (e) it has a stationary entropic density, characterizing a inhomogeneous screening of the medium, obtained from a homotopic version of the H-Theorem.

Keywords: Homotopic deformation; Homotopic random walk; Homotopic Fokker–Planck equation; Inhomogeneous diffusion (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:676:y:2025:i:c:s0378437125004716

DOI: 10.1016/j.physa.2025.130819

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