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Equilibrium fluctuations for a discrete Atlas model

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  • Hernández, Freddy
  • Jara, Milton
  • Valentim, Fábio Júlio

Abstract

We consider a discrete version of the Atlas model, which corresponds to a sequence of zero-range processes on a semi-infinite line, with a source at the origin and a diverging density of particles. We show that the equilibrium fluctuations of this model are governed by a stochastic heat equation with Neumann boundary conditions. As a consequence, we show that the current of particles at the origin converges to a fractional Brownian motion of Hurst exponent H=14.

Suggested Citation

  • Hernández, Freddy & Jara, Milton & Valentim, Fábio Júlio, 2017. "Equilibrium fluctuations for a discrete Atlas model," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 783-802.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:3:p:783-802
    DOI: 10.1016/j.spa.2016.06.026
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    References listed on IDEAS

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    1. Nagahata, Yukio, 2010. "Spectral gap for zero-range processes with jump rate g(x)=x[gamma]," Stochastic Processes and their Applications, Elsevier, vol. 120(6), pages 949-958, June.
    2. Landim, Cláudio & Volchan, Sérgio B., 2000. "Equilibrium fluctuations for a driven tracer particle dynamics," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 139-158, January.
    3. Tomoyuki Ichiba & Vassilios Papathanakos & Adrian Banner & Ioannis Karatzas & Robert Fernholz, 2009. "Hybrid Atlas models," Papers 0909.0065, arXiv.org, revised Apr 2011.
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    Cited by:

    1. Hernández, F. & Jara, M. & Valentim, F., 2020. "Lattice model for fast diffusion equation," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2808-2837.

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