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arXiv · 2103.12253

Stationary measure for the open KPZ equation

Ivan Corwin·Alisa Knizel
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Abstract

We provide the first construction of stationary measures for the open KPZ equation on the spatial interval $[0,1]$ with general inhomogeneous Neumann boundary conditions at $0$ and $1$ depending on real parameters $u$ and $v$, respectively. When $u+v\geq 0$ we uniquely characterize the constructed stationary measures through their multipoint Laplace transform which we prove is given in terms of a stochastic process that we call the continuous dual Hahn process.

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Ivan Corwin, Alisa Knizel. 2021-03-23. Stationary measure for the open KPZ equation. https://arxiv.org/abs/2103.12253

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