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Decoupling and decay of two-point functions in a two-species (T)ASEP
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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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Cited by 1 Pith paper
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Two fluctuating interfaces with sticking interactions: Invariant measures and dynamics
For two identical fluctuating interfaces with sticking at contact points, the exact steady-state measure is an inhomogeneous product form equivalent to the equilibrium Poland-Scheraga DNA denaturation measure.
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