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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.09547 |
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| _version_ | 1866912894205034496 |
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| author | Gess, Benjamin Heydecker, Daniel |
| author_facet | Gess, Benjamin Heydecker, Daniel |
| contents | We consider a zero-range process $η^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t u=\frac12Δu^α, α>1$. As a main result we obtain a large deviation principle in any scaling regime of vanishing particle size $χ_N\to 0$. The key challenge is to develop uniform integrability estimate on the nonlinearity $(η^N(x))^α$ in a situation where neither pathwise regularity nor Dirichlet-form based regularity is readily available. We resolve this by introducing a novel multiscale argument exploiting the appearance of pathwise regularity across scales. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09547 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Porous Medium Equation: Multiscale Integrability in Large Deviations Gess, Benjamin Heydecker, Daniel Probability 60F10 (primary), 82B21 (secondary), 60K35, 82B31 We consider a zero-range process $η^N_t(x)$ with superlinear local jump rate, which in a hydrodynamic-small particle rescaling converges to the porous medium equation $\partial_t u=\frac12Δu^α, α>1$. As a main result we obtain a large deviation principle in any scaling regime of vanishing particle size $χ_N\to 0$. The key challenge is to develop uniform integrability estimate on the nonlinearity $(η^N(x))^α$ in a situation where neither pathwise regularity nor Dirichlet-form based regularity is readily available. We resolve this by introducing a novel multiscale argument exploiting the appearance of pathwise regularity across scales. |
| title | The Porous Medium Equation: Multiscale Integrability in Large Deviations |
| topic | Probability 60F10 (primary), 82B21 (secondary), 60K35, 82B31 |
| url | https://arxiv.org/abs/2602.09547 |