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Article overview
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On microscopic derivation of a fractional stochastic Burgers equation | | Sunder Sethuraman
; | | Date: |
3 Sep 2014 | | Abstract: | We derive from a class of microscopic asymmetric interacting particle systems
on ${mathbb Z}$, with long range jump rates of order $|cdot|^{-(1+alpha)}$
for $0<alpha<2$, different continuum fractional SPDEs. More specifically, we
show the equilibrium fluctuations of the hydrodynamics mass density field of
zero-range processes, depending on the stucture of the asymmetry, and whether
the field is translated with process characteristics velocity, is governed in
various senses by types of fractional stochastic heat or Burgers equations.
The main result: Suppose the jump rate is such that its symmetrization is
long range but its (weak) asymmetry is nearest-neighbor. Then, when
$alpha<3/2$, the fluctuation field in space-time scale $1/alpha:1$,
translated with process characteristic velocity, irrespective of the strength
of the asymmetry, converges to a fractional stochastic heat equation, the limit
also for the symmetric process. However, when $alphageq 3/2$ and the strength
of the weak asymmetry is tuned in scale $1-3/2alpha$, the associated limit
points satisfy a martingale formulation of a fractional stochastic Burgers
equation. | | Source: | arXiv, 1409.0944 | | Services: | Forum | Review | PDF | Favorites | |
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