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The strong Feller property of the open KPZ equation

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arxiv 2211.04466 v1 pith:WKE7QP5X submitted 2022-11-08 math.PR math-phmath.APmath.MP

Alisa Knizel , Konstantin Matetski This is my paper · ORCID
classification math.PRmath-phmath.APmath.MP
keywords equationfellermeasureopenpropertystationarystrongarxiv
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We prove that the semigroup generated by the open KPZ equation on a bounded spatial interval with Neumann boundary conditions parametrized by real parameters u and v enjoys the strong Feller property. From this we conclude that for u+v>0, min(u,v)>-1 the stationary measure constructed in Corwin and Knizel (arXiv:2103.12253) is the unique stationary measure for the equation. It is expected that the same conclusion holds for all values of u and v.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. KPZ equation from open ASEP with general boundary asymmetry

    math.PR 2025-07 conditional novelty 8.0 of 10

    Open ASEP height functions with general local boundary asymmetries converge to the open KPZ equation without Liggett's condition or explicit invariant measures.

  2. On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation

    math.PR 2025-08 unverdicted novelty 7.0 of 10

    The authors identify exact local and uniform spatio-temporal moduli of continuity for nonlinear parabolic SPDEs on bounded intervals and for the open KPZ equation, using new strong local non-determinism proofs under R...

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