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TASEP in half-space
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abstract
In this work, we present the multi-point probability distribution of the totally asymmetric simple exclusion process (TASEP) in a half-space, starting from a general deterministic initial condition. More precisely, let $h(t,x)$ denote the height function of TASEP at position $x$ and time $t$; we provide an explicit formula for \begin{equation*} \mathbb{P}(h(t,y_1)\leq s_1, \ldots, h(t,y_m)\leq s_m). \end{equation*} The formula presented is well-suited for the scaling limit analysis. By applying a 1:2:3 scaling, we derive the probability distribution for the half-space KPZ fixed point, which is conjectured to be the universal process for the limit of the KPZ universality models restricted to a half-space.
Forward citations
Cited by 2 Pith papers
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Periodic directed landscape
The periodic directed landscape is constructed by gluing full-space directed landscapes, and proven to be the universal scaling limit of periodic exponential LPP and of periodic ASEP.
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The half-space KPZ line ensemble and its scaling limit
The half-space KPZ line ensemble is constructed, proven tight under 1:2:3 scaling in critical and supercritical regimes, and shown to have subsequential limits with a one-sided Gibbs property, including pairwise pinne...
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