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On ASEP with Step Bernoulli Initial Condition

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Abstract

This paper extends earlier work on ASEP to the case of step Bernoulli initial condition. The main results are a representation in terms of a Fredholm determinant for the probability distribution of a fixed particle, and asymptotic results which in particular establish KPZ universality for this probability in one regime. (And, as a corollary, for the current fluctuations.)

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Article08 September 2018
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References

  1. Baik, J., Rains, E.M.: Limiting distributions for a polynuclear growth model with external sources. J. Stat. Phys.100, 523–541 (2000)

    Article MATH MathSciNet  Google Scholar 

  2. Baik, J., Ben Arous, G., Péché, S.: Phase transition of the largest eigenvalue for non-null complex sample covariance matrices. Ann. Probab.33, 1643–1697 (2006)

    Article  Google Scholar 

  3. Balázs, M., Quastel, J., Seppäläinen, T.: Scaling exponent for the Hopf-Cole solution of KPZ/stochastic Burgers. PreprintarXiv:0909.4816

  4. Ben Arous, G., Corwin, I.: Current fluctuations for TASEP: a proof of the Prähofer-Spohn conjecture. PreprintarXiv:0905.2993

  5. Borodin, A., Ferrari, P.L., Sasamoto, T.: Two speed TASEP. J. Stat. Phys. (2009). doi:10.1007/s10955-009-9837-7

    Google Scholar 

  6. Ferrari, P.L., Spohn, H.: A determinantal formula for the GOE Tracy-Widom distribution. J. Phys. A: Math. Gen.38, L557–L561 (2005)

    Article MathSciNet ADS  Google Scholar 

  7. Imamura, T., Sasamoto, T.: Fluctuations of the one-dimensional polynuclear growth model with external sources. Nucl. Phys. B699, 503–544 (2004)

    Article MATH MathSciNet ADS  Google Scholar 

  8. Macdonald, I.G.: Symmetric Functions and Hall Polynomials. Clarendon, Oxford (1995)

    MATH  Google Scholar 

  9. Spohn, H.: Kardar-Parisi-Zhang equation in one dimension and line ensembles. Pramana64, 847–857 (2005)

    Article ADS  Google Scholar 

  10. Prähofer, M., Spohn, H.: Current fluctuations in the totally asymmetric simple exclusion process. Prog. Probab.51, 185–204 (2002)

    Google Scholar 

  11. Tracy, C.A., Widom, H.: Integral formulas for the asymmetric simple exclusion process. Commun. Math. Phys.279, 815–844 (2008)

    Article MATH MathSciNet ADS  Google Scholar 

  12. Tracy, C.A., Widom, H.: A Fredholm determinant representation in ASEP. J. Stat. Phys.132, 291–300 (2008)

    Article MATH MathSciNet ADS  Google Scholar 

  13. Tracy, C.A., Widom, H.: Asymptotics in ASEP with step initial condition. Commun. Math. Phys.290, 129–154 (2009)

    Article MathSciNet ADS  Google Scholar 

  14. Tracy, C.A., Widom, H.: Total current fluctuations in ASEP. J. Math. Phys.50, 095204 (2009)

    Article ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, Davis, CA, 95616, USA

    Craig A. Tracy

  2. Department of Mathematics, University of California, Santa Cruz, CA, 95064, USA

    Harold Widom

Authors
  1. Craig A. Tracy

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  2. Harold Widom

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Correspondence toCraig A. Tracy.

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