Equilibrium fluctuations for a discrete Atlas model

Freddy Hernández, Milton Jara and Fábio Júlio Valentim

Stochastic Processes and their Applications, 2017, vol. 127, issue 3, 783-802

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.

Keywords: Atlas model; Zero-range process; Equilibrium fluctuations (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:3:p:783-802

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DOI: 10.1016/j.spa.2016.06.026

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