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

2025/04/01 by Patrik L. Ferrari, Sabrina Gernholt, Ferrari, Patrik L. +1 · 1 citation
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paper · pdf · doi:10.48550/arxiv.2504.00765

Abstract

We consider the two-species totally asymmetric simple exclusion process on 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.

Citations

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