Quantitative hydrodynamics for a generalized contact model
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909213146480640 |
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| author | Amorim, Julian Jara, Milton Xiang, Yangrui |
| author_facet | Amorim, Julian Jara, Milton Xiang, Yangrui |
| contents | We derive a quantitative version of the hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the $L^2$-speed of convergence of the empirical density of states in a generalized contact process defined over a $d$-dimensional torus of size $n$ is of the optimal order $\mathcal O(n^{d/2})$. In addition, we show that the typical fluctuations around the aforementioned hydrodynamic limit are Gaussian, and governed by a inhomogeneous stochastic linear equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_19437 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantitative hydrodynamics for a generalized contact model Amorim, Julian Jara, Milton Xiang, Yangrui Probability Mathematical Physics Biological Physics We derive a quantitative version of the hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the $L^2$-speed of convergence of the empirical density of states in a generalized contact process defined over a $d$-dimensional torus of size $n$ is of the optimal order $\mathcal O(n^{d/2})$. In addition, we show that the typical fluctuations around the aforementioned hydrodynamic limit are Gaussian, and governed by a inhomogeneous stochastic linear equation. |
| title | Quantitative hydrodynamics for a generalized contact model |
| topic | Probability Mathematical Physics Biological Physics |
| url | https://arxiv.org/abs/2405.19437 |