Decoupling and decay of two-point functions in a two-species (T)ASEP
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| Format: | Preprint |
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2025
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| _version_ | 1866911065623756800 |
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| author | Ferrari, Patrik L. Gernholt, Sabrina |
| author_facet | Ferrari, Patrik L. Gernholt, Sabrina |
| contents | We consider the two-species totally asymmetric simple exclusion process on $\mathbb{Z}$ with a translation-invariant stationary measure as the initial condition. We establish the asymptotic decoupling of the marginal height profiles along characteristic lines and prove the decay of the two-point functions in the large-time limit, thus confirming predictions of the nonlinear fluctuating hydrodynamics theory. Our approach builds on the queueing construction of the stationary measure introduced in [Angel'06, Ferrari-Martin'07] and extends the theory of backwards paths for height functions developed in [Bufetov-Ferrari'22, Ferrari-Nejjar'24]. The arguments for asymptotic decoupling also apply to further homogeneous initial data, and the decay of the two-point functions is proven for the stationary two-species asymmetric simple exclusion process, beyond the totally asymmetric case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decoupling and decay of two-point functions in a two-species (T)ASEP Ferrari, Patrik L. Gernholt, Sabrina Probability We consider the two-species totally asymmetric simple exclusion process on $\mathbb{Z}$ with a translation-invariant stationary measure as the initial condition. We establish the asymptotic decoupling of the marginal height profiles along characteristic lines and prove the decay of the two-point functions in the large-time limit, thus confirming predictions of the nonlinear fluctuating hydrodynamics theory. Our approach builds on the queueing construction of the stationary measure introduced in [Angel'06, Ferrari-Martin'07] and extends the theory of backwards paths for height functions developed in [Bufetov-Ferrari'22, Ferrari-Nejjar'24]. The arguments for asymptotic decoupling also apply to further homogeneous initial data, and the decay of the two-point functions is proven for the stationary two-species asymmetric simple exclusion process, beyond the totally asymmetric case. |
| title | Decoupling and decay of two-point functions in a two-species (T)ASEP |
| topic | Probability |
| url | https://arxiv.org/abs/2504.00765 |