Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks

Abstract

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 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.

Published at http://dx.doi.org/10.1214/009117904000000946 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Shape Fluctuations and Random Matrices
• Strong law of large numbers for the interface in ballistic deposition
• Diffusive fluctuations for one-dimensional totally asymmetric interacting random dynamics

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• Hammersley's harness process: invariant distributions and height fluctuations
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• Fluctuations of the empirical quantiles of independent Brownian motions
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