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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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