Hydrodynamic limit for Glauber-Kawasaki dynamics on the Sierpiński gasket
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908847116910592 |
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| author | van Meurs, Patrick Tsunoda, Kenkichi |
| author_facet | van Meurs, Patrick Tsunoda, Kenkichi |
| contents | We prove the hydrodynamic limit for Glauber-Kawasaki dynamics on the Sierpiński gasket, a prototypical fractal graph that lacks translational invariance. The main novelty lies in incorporating Glauber dynamics, allowing for particle creation and annihilation with birth-death rates depending locally on the particle configuration. In the macroscopic limit, the particle density evolves according to a nonlinear reaction--diffusion equation, where the reaction term is explicitly determined by the microscopic rates. The key new ingredient is a replacement lemma adapted to the fractal geometry of the Sierpiński gasket. We establish this lemma by deriving 1-block and 2-blocks estimates on the Sierpiński gasket graph, which require new arguments due to the absence of classical lattice structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit for Glauber-Kawasaki dynamics on the Sierpiński gasket van Meurs, Patrick Tsunoda, Kenkichi Probability 60K35, 82C22, 28A80 We prove the hydrodynamic limit for Glauber-Kawasaki dynamics on the Sierpiński gasket, a prototypical fractal graph that lacks translational invariance. The main novelty lies in incorporating Glauber dynamics, allowing for particle creation and annihilation with birth-death rates depending locally on the particle configuration. In the macroscopic limit, the particle density evolves according to a nonlinear reaction--diffusion equation, where the reaction term is explicitly determined by the microscopic rates. The key new ingredient is a replacement lemma adapted to the fractal geometry of the Sierpiński gasket. We establish this lemma by deriving 1-block and 2-blocks estimates on the Sierpiński gasket graph, which require new arguments due to the absence of classical lattice structures. |
| title | Hydrodynamic limit for Glauber-Kawasaki dynamics on the Sierpiński gasket |
| topic | Probability 60K35, 82C22, 28A80 |
| url | https://arxiv.org/abs/2602.19059 |