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- W1644186056 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." @default.
- W1644186056 created "2016-06-24" @default.
- W1644186056 creator A5070645286 @default.
- W1644186056 date "2015-12-08" @default.
- W1644186056 modified "2023-10-18" @default.
- W1644186056 title "On Microscopic Derivation of a Fractional Stochastic Burgers Equation" @default.
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- W1644186056 doi "https://doi.org/10.1007/s00220-015-2524-4" @default.
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