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Thermodynamic limit for the invariant measures in supercritical zero range processes
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  • Published: 06 August 2008

Thermodynamic limit for the invariant measures in supercritical zero range processes

  • Inés Armendáriz1,2 &
  • Michail Loulakis3,4 

Probability Theory and Related Fields volume 145, pages 175–188 (2009)Cite this article

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Abstract

We prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles. It is known that in this case there is a single site that accomodates a macroscopically large number of the particles in the system. We show that in the thermodynamic limit the rest of the sites have joint distribution equal to the grand canonical measure at the critical density. This improves the result of Großkinsky, Schütz and Spohn, where convergence is obtained for the finite dimensional marginals. We obtain as corollaries limit theorems for the order statistics of the components and for the fluctuations of the bulk.

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Author information

Authors and Affiliations

  1. IME, Universidade de São Paulo, Sao Paulo, Brazil

    Inés Armendáriz

  2. Universidad de San Andrés, Vito Dumas 284, B1644BID, Victoria, Argentina

    Inés Armendáriz

  3. Department of Applied Mathematics, University of Crete, Knossos Avenue, 714 09, Heraklion, Crete, Greece

    Michail Loulakis

  4. Institute of Applied and Computational Mathematics, FORTH Crete, Knossos Avenue, 714 09, Heraklion, Crete, Greece

    Michail Loulakis

Authors
  1. Inés Armendáriz
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  2. Michail Loulakis
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Correspondence to Inés Armendáriz.

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Armendáriz, I., Loulakis, M. Thermodynamic limit for the invariant measures in supercritical zero range processes. Probab. Theory Relat. Fields 145, 175–188 (2009). https://doi.org/10.1007/s00440-008-0165-7

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  • Received: 02 February 2008

  • Revised: 02 June 2008

  • Published: 06 August 2008

  • Issue Date: September 2009

  • DOI: https://doi.org/10.1007/s00440-008-0165-7

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Keywords

  • Condensation
  • Equivalence of ensembles
  • Large deviations
  • Subexponential distributions
  • Zero range processes

Mathematics Subject Classification (2000)

  • 60K35
  • 82C22
  • 60F10
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