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Discrete Polynuclear Growth and Determinantal Processes

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Abstract

We consider a discrete polynuclear growth (PNG) process and prove a functional limit theorem for its convergence to the Airy process. This generalizes previous results by Prähofer and Spohn. The result enables us to express the F 1 GOE Tracy- Widom distribution in terms of the Airy process. We also show some results, and give a conjecture, about the transversal fluctuations in a point to line last passage percolation problem. Furthermore we discuss a rather general class of measures given by products of determinants and show that these measures have determinantal correlation functions.

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Authors and Affiliations

  1. Department of Mathematics, Royal Institute of Technology, 100 44, Stockholm, Sweden

    Kurt Johansson

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  1. Kurt Johansson
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Correspondence to Kurt Johansson.

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Communicated by H. Spohn

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Johansson, K. Discrete Polynuclear Growth and Determinantal Processes. Commun. Math. Phys. 242, 277–329 (2003). https://doi.org/10.1007/s00220-003-0945-y

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  • DOI: https://doi.org/10.1007/s00220-003-0945-y

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