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March 2005 Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks
Timo Seppäläinen
Ann. Probab. 33(2): 759-797 (March 2005). DOI: 10.1214/009117904000000946

Abstract

Fluctuations from a hydrodynamic limit of a one-dimensional asymmetric system come at two levels. On the central limit scale n1/2 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 n1/4 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 n1/3, as has been discovered through related combinatorial growth models.

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Timo Seppäläinen. "Second-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks." Ann. Probab. 33 (2) 759 - 797, March 2005. https://doi.org/10.1214/009117904000000946

Information

Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1108.60083
MathSciNet: MR2123209
Digital Object Identifier: 10.1214/009117904000000946

Subjects:
Primary: 60K35
Secondary: 60F17

Keywords: Fluctuations , fractional Brownian motion , Hammersley’s process , Hydrodynamic limit , Independent random walks

Rights: Copyright © 2005 Institute of Mathematical Statistics

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Vol.33 • No. 2 • March 2005
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