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Type: Artigo de periódico
Title: Time fluctuations of the random average process with parabolic initial conditions
Author: Fontes, LRG
Medeiros, DP
Vachkovskaia, M
Abstract: The random average process is a randomly evolving d-dimensional surface whose heights are updated by random convex combinations of neighboring heights. The fluctuations of this process in case of linear initial conditions have been studied before. In this paper, we analyze the case of polynomial initial conditions of degree 2 and higher. Specifically, we prove that the time fluctuations of a initial parabolic surface are of order n(2-d/2) for d=1,2,3; log n in d=4; and are bounded in d greater than or equal to 5. We establish a central limit theorem in d = 1. In the bounded case of d greater than or equal to 5, we exhibit an invariant measure for the process as seen from the average height at the origin and describe its asymptotic space fluctuations. We consider briefly the case of initial polynomial surfaces of higher degree to show that their time fluctuations are not bounded in high dimensions, in contrast with the linear and parabolic cases. (C) 2002 Elsevier Science B.V. All rights reserved.
Subject: random average process
random surfaces
harness process
linear process
surface fluctuations
central limit theorem
Country: Holanda
Editor: Elsevier Science Bv
Citation: Stochastic Processes And Their Applications. Elsevier Science Bv, v. 103, n. 2, n. 257, n. 276, 2003.
Rights: fechado
Identifier DOI: 10.1016/S0304-4149(02)00210-7
Date Issue: 2003
Appears in Collections:Unicamp - Artigos e Outros Documentos

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