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Fluctuation–dissipation equation of asymmetric simple exclusion processes
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  • Published: July 1997

Fluctuation–dissipation equation of asymmetric simple exclusion processes

  • C. Landim1 &
  • H. T. Yau3 

Probability Theory and Related Fields volume 108, pages 321–356 (1997)Cite this article

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Summary.

We consider asymmetric simple exclusion processes on the lattice Zopf;d in dimension d≥3. We denote by L the generator of the process, ∇ the lattice gradient, η the configuration, and w the current of the dynamics associated to the conserved quantity. We prove that the fluctuation–dissipation equation w=Lu+D∇η has a solution for some function u and some constant D identified to be the diffusion coefficient. Intuitively, Lu represents rapid fluctuation and this equation describes a decomposition of the current into fluctuation and gradient of the density field, representing the dissipation. Using this result, we proved rigorously that the Green-Kubo formula converges and it can be identified as the diffusion coefficient.

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Authors and Affiliations

  1. IMPA, Estrada Dona Castorina 110, CEP 22460 Rio de Janeiro, Brasil, , , , ,

    C. Landim

  2. Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, , , , ,

    H. T. Yau

Authors
  1. C. Landim
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  2. H. T. Yau
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Received: 14 May 1996 / In revised form: 20 February 1997

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Landim, C., Yau, H. Fluctuation–dissipation equation of asymmetric simple exclusion processes. Probab Theory Relat Fields 108, 321–356 (1997). https://doi.org/10.1007/s004400050112

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  • Issue Date: July 1997

  • DOI: https://doi.org/10.1007/s004400050112

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  • Mathematics Subject Classification (1991): 60k35 82A05
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