Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910215163609088 |
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| author | Górska, K. Horzela, A. Maširević, D. Jankov Pietrzak, T. Pogány, 1T. K. Sandev, T. |
| author_facet | Górska, K. Horzela, A. Maširević, D. Jankov Pietrzak, T. Pogány, 1T. K. Sandev, T. |
| contents | 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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14727 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model Górska, K. Horzela, A. Maširević, D. Jankov Pietrzak, T. Pogány, 1T. K. Sandev, T. Mathematical Physics 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. 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. |
| title | Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2602.14727 |