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Metastability of reversible condensed zero range processes on a finite set
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  • Published: 12 January 2011

Metastability of reversible condensed zero range processes on a finite set

  • J. Beltrán1,2 &
  • C. Landim3,4 

Probability Theory and Related Fields volume 152, pages 781–807 (2012)Cite this article

  • 247 Accesses

  • 38 Citations

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Abstract

Let \({r: S\times S\to \mathbb R_{+}}\) be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m. For α > 1, let \({g: \mathbb N\to \mathbb R_{+}}\) be given by g(0) = 0, g(1) = 1, g(k) =  (k/k − 1)α, k ≥ 2. Consider a zero range process on S in which a particle jumps from a site x, occupied by k particles, to a site y at rate g(k)r (x, y). Let N stand for the total number of particles. In the stationary state, as \({N\uparrow\infty}\) , all particles but a finite number accumulate on one single site. We show in this article that in the time scale N 1+α the site which concentrates almost all particles evolves as a random walk on S whose transition rates are proportional to the capacities of the underlying random walk.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques, École Polytechnique Fédérale de Lausanne, Station 8, 1015, Lausanne, Switzerland

    J. Beltrán

  2. PUCP, Av. Universitaria cdra. 18, San Miguel, Ap. 1761, Lima, 100, Peru

    J. Beltrán

  3. IMPA, Estrada Dona Castorina 110, CEP 22460, Rio de Janeiro, Brazil

    C. Landim

  4. CNRS UMR 6085, Université de Rouen, Avenue de l’Université, BP. 12, Technopôle du Madrillet, 76801, Saint-Étienne-du-Rouvray, France

    C. Landim

Authors
  1. J. Beltrán
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  2. C. Landim
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Correspondence to C. Landim.

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Cite this article

Beltrán, J., Landim, C. Metastability of reversible condensed zero range processes on a finite set. Probab. Theory Relat. Fields 152, 781–807 (2012). https://doi.org/10.1007/s00440-010-0337-0

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  • Received: 22 December 2009

  • Accepted: 23 November 2010

  • Published: 12 January 2011

  • Issue Date: April 2012

  • DOI: https://doi.org/10.1007/s00440-010-0337-0

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Keywords

  • Metastability
  • Condensation
  • Zero range processes

Mathematics Subject Classification (2000)

  • 60K35
  • 82C20
  • 82B26
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