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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. ; ( , Communications in Mathematical Physics)
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  3. ; ( , Probability and Mathematical Physics)
    Free, publicly-accessible full text available January 1, 2025
  4. ; ( , The Annals of Probability)
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  5. ; ; ( , Advances in Mathematics)
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  6. ; ; ( , Communications in Mathematical Physics)
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  7. ; ; ; ( , Electronic Journal of Probability)
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  8. ; ( , Probability Theory and Related Fields)
    null (Ed.)
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  9. ; ; ( , The Annals of Probability)
    null (Ed.)
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  10. ( , Advanced studies in pure mathematics)
    null (Ed.)
    We prove that the values of discrete directed polymer partition functions involving multiple non-intersecting paths remain invariant under replacing the background weights by their images under the geometric RSK correspondence. This result is inspired by a recent and remarkable identity proved by Dauvergne, Orthmann and Virag which is recovered as the zero-temperature, semi-discrete limit of our main result. 
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