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Asymmetric Simple Exclusion Process with Open Boundaries and Koornwinder Polynomials

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Abstract

In this paper, we analyze the steady state of the asymmetric simple exclusion process with open boundaries and second class particles by deforming it through the introduction of spectral parameters. The (unnormalized) probabilities of the particle configurations get promoted to Laurent polynomials in the spectral parameters and are constructed in terms of non-symmetric Koornwinder polynomials. In particular, we show that the partition function coincides with a symmetric Macdonald–Koornwinder polynomial. As an outcome, we compute the steady current and the average density of first class particles.

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Authors and Affiliations

  1. CNRS UMR 8089, LPTM, Université de Cergy-Pontoise, Cergy-Pontoise Cedex, France

    Luigi Cantini

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  1. Luigi Cantini
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Correspondence to Luigi Cantini.

Additional information

Communicated by Jean-Michel Maillet.

The work of LC is partially supported by CNRS through a “Chaire d’excellence.” It is a pleasure to thank Jan de Gier for collaboration at an early stage of this project and the Department of Mathematics and Statistics of the University of Melbourne for kind hospitality.

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Cantini, L. Asymmetric Simple Exclusion Process with Open Boundaries and Koornwinder Polynomials. Ann. Henri Poincaré 18, 1121–1151 (2017). https://doi.org/10.1007/s00023-016-0540-3

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  • DOI: https://doi.org/10.1007/s00023-016-0540-3

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