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Pré-Publication, Document De Travail Année : 2023

Markov duality and Bethe ansatz formula for half-line open ASEP

Résumé

Using a Markov duality satisfied by ASEP on the integer line, we deduce a similar Markov duality for half-line open ASEP and open ASEP on a segment. This leads to closed systems of ODEs characterizing observables of the models. In the half-line case, we solve the system of ODEs using Bethe ansatz and prove an integral formula for $q$-moments of the current at $n$ distinct spatial locations. We then use this formula to confirm predictions for the moments of the multiplicative noise stochastic heat equation on $\mathbb R_{>0}$ with Robin type boundary condition and we obtain new formulas in the case of a Dirichlet boundary condition.

Dates et versions

hal-04257113 , version 1 (24-10-2023)

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Guillaume Barraquand, Ivan Corwin. Markov duality and Bethe ansatz formula for half-line open ASEP. 2023. ⟨hal-04257113⟩
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