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arXiv · 2504.00765

Decoupling and decay of two-point functions in a two-species (T)ASEP

Patrik L. Ferrari·Sabrina Gernholt
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Abstract

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.

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Patrik L. Ferrari, Sabrina Gernholt. 2025-04-01. Decoupling and decay of two-point functions in a two-species (T)ASEP. https://doi.org/10.1007/s11040-026-09580-0

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