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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2502.14590 |
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| _version_ | 1866909503032655872 |
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| author | Gomez, Ignacio S de Jesus, Daniel Rocha Thibes, Ronaldo |
| author_facet | Gomez, Ignacio S de Jesus, Daniel Rocha Thibes, Ronaldo |
| contents | 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 nonexensive 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, according to deformation and homotopic parameters. The HFPE obtained from associated master equation to the HRW presents the features: a) it results an special case of the van Kampen diffusion equation (5) of Ref. [N. G. van Kampen, \emph{Z. Phys. B Condensed Matter} \textbf{68}, 135 (1987)]; b) it exhibits a superdiffusion in function of deformation and homotopic parameters; 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_14590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random walks with homotopic spatial inhomogeneities Gomez, Ignacio S de Jesus, Daniel Rocha Thibes, Ronaldo Mathematical Physics Data Analysis, Statistics and Probability 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 nonexensive 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, according to deformation and homotopic parameters. The HFPE obtained from associated master equation to the HRW presents the features: a) it results an special case of the van Kampen diffusion equation (5) of Ref. [N. G. van Kampen, \emph{Z. Phys. B Condensed Matter} \textbf{68}, 135 (1987)]; b) it exhibits a superdiffusion in function of deformation and homotopic parameters; 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. |
| title | Random walks with homotopic spatial inhomogeneities |
| topic | Mathematical Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2502.14590 |