Stationary measure for the open KPZ equation

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 $u+v\ge 0$ 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.

version accepted for publication in CPAM, 90 pages, 5 figures; Mistake in statement and proof of Proposition 2.3 remedied

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