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  1. ; ( , Communications on Pure and Applied Mathematics)
    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 parametersuandv, respectively. When , 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. Our work relies on asymptotic analysis of Bryc and Wesołowski's Askey–Wilson process formulas for the open ASEP stationary measure (which in turn arise from Uchiyama, Sasamoto and Wadati's Askey‐Wilson Jacobi matrix representation of Derrida et al.'s matrix product ansatz) in conjunction with Corwin and Shen's proof that open ASEP converges to open KPZ under weakly asymmetric scaling.

     
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    Free, publicly-accessible full text available April 1, 2025
  2. ( , Stochastic Processes and their Applications)
    Free, publicly-accessible full text available March 1, 2025
  3. ; ( , The Annals of Probability)
    Free, publicly-accessible full text available September 1, 2024
  4. ; ; ( , Advances in Mathematics)
    Free, publicly-accessible full text available June 1, 2024
  5. ; ; ( , Communications in Mathematical Physics)
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  6. ; ; ; ( , Physical Review E)
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  7. ; ; ; ( , Electronic Journal of Probability)
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  8. ( , Toeplitz Operators and Random Matrices)
    Accepted Manuscript Full Text Available
  9. ; ; ( , Probability Theory and Related Fields)
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  10. ; ( , Annales de l'Institut Henri Poincaré, Probabilités et Statistiques)
    null (Ed.)
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