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Creators/Authors contains: "Quastel, Jeremy"

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  1. ; ; (, Journal of the European Mathematical Society)
    It is shown that the polynuclear growth model is a completely integrable Markov process in the sense that its transition probabilities are given by Fredholm determinants of kernels produced by a scattering transform based on the invariant measures modulo the absolute height, continuous time simple random walks. From the linear evolution of the kernels, it is shown that then-point distributions are determinants ofn\times nmatrices evolving according to thetwo-dimensional non-Abelian Toda lattice. 
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    Free, publicly-accessible full text available January 3, 2026
  2. ; (, Communications on Pure and Applied Mathematics)
    Abstract We consider the large deviations from the hydrodynamic limit of the Totally Asymmetric Simple Exclusion Process (TASEP). This problem was studied by Jensen and Varadhan and was shown to be related to entropy production in the inviscid Burgers equation. Here we prove the full large deviation principle. Our method relies on the explicit formula of Matetski, Quastel, and Remenik for the transition probabilities of the TASEP. 
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  3. ; ; (, Transactions of the American Mathematical Society, Series B)
    We study the stochastic Korteweg-de Vries equation (SKdV) with an additive space-time white noise forcing, posed on the one-dimensional torus. In particular, we construct global-in-time solutions to SKdV with spatial white noise initial data. Due to the lack of an invariant measure, Bourgain’s invariant measure argument is not applicable to this problem. In order to overcome this difficulty, we implement a variant of Bourgain’s argument in the context of an evolution system of measures and construct global-in-time dynamics. Moreover, we show that the white noise measure with variance 1 + t 1+t is an evolution system of measures for SKdV with the white noise initial data. 
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    Full Text Available 
  4. ; ; (, Acta Mathematica)
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  5. ; ; (, Probability and Mathematical Physics)
    null (Ed.)
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