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Heterogeneous Cattaneo–Vernotte equation connection to the noisy voter model

Year: 2026
Type: article
Abstract: We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic interpretations of the heterogeneous diffusion process. The heterogeneity in the system is introduced by considering a position-dependent diffusion coefficient. The exact results for the probability density function and the mean-squared displacement are provided. The limiting case of heterogeneous diffusion is analyzed in detail, and the corresponding time-averaged mean-squared displacement is calculated. From the obtained results, an ergodicity breaking is observed.
DOI: 10.1063/5.0325574
Authors: K. Górska, A. Horzela, D. Jankov Maširević, T. Pietrzak, T. K. Pogány, T. Sandev
Institutions: Institute of Nuclear Physics, Polish Academy of Sciences, Polish Academy of Sciences, University of Osijek, Obuda University, University of Rijeka, Macedonian Academy of Sciences and Arts, Korea University, Ss. Cyril and Methodius University in Skopje
Language: English
Open Access status: green
OpenAlex ID: W7150974992
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Cites: 68
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