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Creators/Authors contains: "Knizel, Alisa"

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  1. ; (, Selecta Mathematica)
    Abstract The goal of the paper is to introduce a new set of tools for the study of discrete and continuous$$\beta $$ β -corners processes. In the continuous setting, our work provides a multi-level extension of the loop equations (also called Schwinger–Dyson equations) for$$\beta $$ β -log gases obtained by Borot and Guionnet in (Commun. Math. Phys. 317, 447–483, 2013). In the discrete setting, our work provides a multi-level extension of the loop equations (also called Nekrasov equations) for discrete$$\beta $$ β -ensembles obtained by Borodin, Gorin and Guionnet in (Publications mathématiques de l’IHÉS 125, 1–78, 2017). 
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    Free, publicly-accessible full text available February 1, 2026
  2. ; (, 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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    Full Text Available 
  3. ; ; (, Communications in Mathematical Physics)
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  4. ; (, Journal of Functional Analysis)
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  5. ; (, International Mathematics Research Notices)
    Abstract The goal of this paper is to investigate the missing part of the story about the relationship between the orthogonal polynomial ensembles and Painlevé equations. Namely, we consider the $$q$$-Racah polynomial ensemble and show that the one-interval gap probabilities in this case can be expressed through a solution of the discrete $$q$$-P$$\left (E_7^{(1)}/A_{1}^{(1)}\right )$$ equation. Our approach also gives a new Lax pair for this equation. This Lax pair has an interesting additional involutive symmetry structure. 
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