In the Jack limit $q=t^{\beta/2}\to1$ the absorbing wall disappears, and the Macdonald noncolliding walks turn into the $\beta$-noncolliding random walks studied by Huang [arXiv:1708.07115]. Taking $q=0$ (Hall-Littlewood degeneration) and further sending $t\to 1$, we obtain a continuous time particle system on $\mathbb{Z}_{\ge0}$ with inhomogeneous jump rates and absorbing wall at zero.

]]>Our dynamics arise naturally from the Yang-Baxter equation for the six vertex model via its bijectivisation, a technique first used in Bufetov-Petrov (arXiv:1712.04584). The dynamics we construct are irreversible; in particular, the height function has a nonzero average drift. In each KPZ pure state, we explicitly compute the average drift (also known as the current) as a function of the slope. We use this to analyze the hydrodynamics of a non-stationary version of our process acting on quarter plane stochastic six vertex configurations. The fixed-time limit shapes in the quarter plane model were obtained in Borodin-Corwin-Gorin (arXiv:1407.6729).

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]]>In the spirit of the theory of Schur processes, we define probability measures on sequences of signatures with probability weights proportional to products of our symmetric functions. We show that these measures can be viewed as determinantal point processes, and we express their correlation kernels in a double contour integral form. We present two proofs: The first is a direct computation of Eynard–Mehta type, and the second uses non-standard, inhomogeneous versions of fermionic operators in a Fock space coming from the algebraic Bethe Ansatz for the six vertex model.

We also interpret our determinantal processes as random domino tilings of a half-strip with inhomogeneous domino weights. In the bulk, we show that the lattice asymptotic behavior of such domino tilings is described by a new determinantal point process on $\mathbb{Z}^{2}$, which can be viewed as an doubly-inhomogeneous generalization of the extended discrete sine process.

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