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Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks. (English) Zbl 1108.60083
Summary: Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale $$n^{1/2}$$ one sees initial fluctuations transported along characteristics and no dynamical noise. The second order of fluctuations comes from the particle current across the characteristic. For a system made up of independent random walks we show that the second-order fluctuations appear at scale $$n^{1/4}$$ and converge to a certain self-similar Gaussian process. If the system is in equilibrium, this limiting process specializes to fractional Brownian motion with Hurst parameter $$1/4$$. This contrasts with the asymmetric exclusion and Hammersley’s process whose second-order fluctuations appear at scale $$n^{1/3}$$, as has been discovered through related combinatorial growth models.

##### MSC:
 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60F17 Functional limit theorems; invariance principles 82C22 Interacting particle systems in time-dependent statistical mechanics
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