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Equilibrium fluctuations of asymmetric simple exclusion processes in dimension d≥3
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  • Published: March 2001

Equilibrium fluctuations of asymmetric simple exclusion processes in dimension d≥3

  • Chih-Chung Chang1,
  • Claudio Landim2 &
  • Stefano Olla3 

Probability Theory and Related Fields volume 119, pages 381–409 (2001)Cite this article

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  • 22 Citations

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Abstract.

We consider an asymmetric exclusion process in dimension d≥ 3 under diffusive rescaling starting from the Bernoulli product measure with density 0 < α < 1. We prove that the density fluctuation field Y N t converges to a generalized Ornstein–Uhlenbeck process, which is formally the solution of the stochastic differential equatin dY t = ?Y t dt + dB ∇ t , where ? is a second order differential operator and B ∇ t is a mean zero Gaussian field with known covariances.

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Authors and Affiliations

  1. Department of Mathematics, National Taiwan University, Taipei, Taiwan, R.O.C. e-mail: ccchang@math.ntu.edu.tw, , , , , , CN

    Chih-Chung Chang

  2. IMPA-Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botanico, CEP 22460, Rio de Janeiro, Brasil and CNRS UPRES-A 6085, Université de Rouen, 76.128 Mont Saint Aignan Cedex, France. e-mail: landim@impa.br, , , , , , BR

    Claudio Landim

  3. Département de Mathématiques, Université de Cergy–Pontoise, 2 Av. Adolphe Chauvin, BP 222, Pontoise 95.302 Cergy–Pontoise Cedex, France and CMAP, Ecole Polytechnique 91128 Palaiseau cedex, France. e-mail: olla@math.u-cergy.fr, , , , , , FR

    Stefano Olla

Authors
  1. Chih-Chung Chang
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  2. Claudio Landim
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  3. Stefano Olla
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Additional information

Received: 31 May 1999 / Revised version: 15 June 2000 / Published online: 24 January 2001

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Cite this article

Chang, CC., Landim, C. & Olla, S. Equilibrium fluctuations of asymmetric simple exclusion processes in dimension d≥3. Probab Theory Relat Fields 119, 381–409 (2001). https://doi.org/10.1007/PL00008764

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  • Issue Date: March 2001

  • DOI: https://doi.org/10.1007/PL00008764

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  • Mathematics Subject Classification (2000): Primary 60K35; Secondary 82A05
  • Key words or phrases: Equilibrium fluctuations – Asymmetric exclusion processes – Hydrodynamic limit
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