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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.21933 |
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| _version_ | 1866917821528670208 |
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| author | Ayala, Mario Zimmer, Johannes |
| author_facet | Ayala, Mario Zimmer, Johannes |
| contents | We consider a d-dimensional symmetric inclusion process (SIP), where particles are allowed to jump arbitrarily far apart. We establish both the hydrodynamic limit and non-equilibrium fluctuations for the empirical measure of particles. With the help of self-duality and Mosco convergence of Dirichlet forms, we extend structural parallels between exclusion and inclusion dynamics from the short-range scenario to the long-range setting. The hydrodynamic equation for the symmetric inclusion process turns out to be of non-local type. At the level of fluctuations from the hydrodynamic limit, we demonstrate that the density fluctuation field converges to a time-dependent generalized Ornstein-Uhlenbeck process whose characteristics are again non-local. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21933 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limits and non-equilibrium fluctuations for the Symmetric Inclusion Process with long jumps Ayala, Mario Zimmer, Johannes Probability We consider a d-dimensional symmetric inclusion process (SIP), where particles are allowed to jump arbitrarily far apart. We establish both the hydrodynamic limit and non-equilibrium fluctuations for the empirical measure of particles. With the help of self-duality and Mosco convergence of Dirichlet forms, we extend structural parallels between exclusion and inclusion dynamics from the short-range scenario to the long-range setting. The hydrodynamic equation for the symmetric inclusion process turns out to be of non-local type. At the level of fluctuations from the hydrodynamic limit, we demonstrate that the density fluctuation field converges to a time-dependent generalized Ornstein-Uhlenbeck process whose characteristics are again non-local. |
| title | Hydrodynamic limits and non-equilibrium fluctuations for the Symmetric Inclusion Process with long jumps |
| topic | Probability |
| url | https://arxiv.org/abs/2410.21933 |