Relaxation to equilibrium of conservative dynamics II: non-gradient exclusion processes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912604344025088 |
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| author | Gu, Chenlin Yang, Linzhi |
| author_facet | Gu, Chenlin Yang, Linzhi |
| contents | For the speed-change exclusion process on $\mathbb{Z}^d$ reversible with respect to the product Bernoulli measure, we prove that its semigroup $P_t$ satisfies a variance decay $\operatorname{Var}[P_t u] = C_u t^{-\frac{d}{2}} + o(t^{-\frac{d+δ}{2}})$ for every local function $u$, with the constant $C_u$ explicitly characterized. This extends the result of Janvresse, Landim, Quastel and Yau in [Ann. Probab. 27(1) 325--360, 1999] to a non-gradient model. The proof combines the regularization argument in the previous work, and the chaos expansion in [Markov Process. Related Fields, 5(2) 125--162, 1999] by Bertini and Zegarlinski, via a new input from the homogenization theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_20797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relaxation to equilibrium of conservative dynamics II: non-gradient exclusion processes Gu, Chenlin Yang, Linzhi Probability Analysis of PDEs 82C22, 35B27, 60K35 For the speed-change exclusion process on $\mathbb{Z}^d$ reversible with respect to the product Bernoulli measure, we prove that its semigroup $P_t$ satisfies a variance decay $\operatorname{Var}[P_t u] = C_u t^{-\frac{d}{2}} + o(t^{-\frac{d+δ}{2}})$ for every local function $u$, with the constant $C_u$ explicitly characterized. This extends the result of Janvresse, Landim, Quastel and Yau in [Ann. Probab. 27(1) 325--360, 1999] to a non-gradient model. The proof combines the regularization argument in the previous work, and the chaos expansion in [Markov Process. Related Fields, 5(2) 125--162, 1999] by Bertini and Zegarlinski, via a new input from the homogenization theory. |
| title | Relaxation to equilibrium of conservative dynamics II: non-gradient exclusion processes |
| topic | Probability Analysis of PDEs 82C22, 35B27, 60K35 |
| url | https://arxiv.org/abs/2509.20797 |