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

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dc.creatorSeppalainen, Timo
dc.date2003-10-03
dc.date2005-04-06
dc.date.accessioned2026-07-07T05:01:36Z
dc.date.available2026-07-07T05:01:36Z
dc.descriptionFluctuations 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.
dc.descriptionPublished 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)
dc.identifierhttps://arxiv.org/abs/math/0310044
dc.identifierhttp://arxiv.org/abs/math/0310044
dc.identifierAnnals of Probability 2005, Vol. 33, No. 2, 759-797
dc.identifierdoi:10.1214/009117904000000946
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/68737
dc.subjectProbability
dc.subject60K35 (Primary) 60F17. (Secondary)
dc.titleSecond-order fluctuations and current across characteristic for a one-dimensional growth model of independent random walks
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