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Phase transition in equilibrium fluctuations of symmetric slowed exclusion

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  • Franco, Tertuliano
  • Gonçalves, Patrícia
  • Neumann, Adriana

Abstract

We analyze the equilibrium fluctuations of density, current and tagged particle in symmetric exclusion with a slow bond. The system evolves in the one-dimensional lattice and the jump rate is everywhere equal to one except at the slow bond where it is αn−β, with α>0, β∈[0,+∞] and n is the scaling parameter. Depending on the regime of β, we find three different behaviors for the limiting fluctuations whose covariances are explicitly computed. In particular, for the critical value β=1, starting a tagged particle near the slow bond, we obtain a family of Gaussian processes indexed in α, interpolating a fractional Brownian motion of Hurst exponent 1/4 and the degenerate process equal to zero.

Suggested Citation

  • Franco, Tertuliano & Gonçalves, Patrícia & Neumann, Adriana, 2013. "Phase transition in equilibrium fluctuations of symmetric slowed exclusion," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4156-4185.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:12:p:4156-4185
    DOI: 10.1016/j.spa.2013.06.016
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    References listed on IDEAS

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    1. Gonçalves, Patrícia, 2008. "Central limit theorem for a tagged particle in asymmetric simple exclusion," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 474-502, March.
    2. Farfan, Jonathan & Simas, Alexandre B. & Valentim, Fábio J., 2010. "Equilibrium fluctuations for exclusion processes with conductances in random environments," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1535-1562, August.
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    Cited by:

    1. Franco, Tertuliano & Gonçalves, Patrícia & Neumann, Adriana, 2019. "Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1413-1442.
    2. Cardoso, Pedro & Gonçalves, Patrícia & Jiménez-Oviedo, Byron, 2023. "Diffusive fluctuations of long-range symmetric exclusion with a slow barrier," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    3. Franco, Tertuliano & Gonçalves, Patrícia & Schütz, Gunter M., 2016. "Scaling limits for the exclusion process with a slow site," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 800-831.

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