F. Hernández, M. Jara, Fabio J. Valentim
Published 2015-07-16Version 1
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=1/4.
A connection between the stochastic heat equation and fractional Brownian motion, and a simple proof of a result of Talagrand
Equilibrium fluctuations for the slow boundary exclusion process
Equilibrium fluctuations for the zero-range process on the Sierpinski gasket
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