Exceptional times for the dynamical discrete web

Autor(es)

Fontes, L. R. G. ^[1] ; Newman, C. M. ^[2] ; Ravishankar, K. ^[3] ; Schertzer, E. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05508 Sao Paulo - Brazil

^[2] NYU, Courant Inst Math Sci, New York, NY 10012 - USA

^[3] SUNY Albany, Dept Math, New Paltz, NY 12561 - USA

^[4] Columbia Univ, Dept Math, New York, NY 10027 - USA

• Tipo de documento: Artigo Científico
• Fonte: Stochastic Processes and their Applications; v. 119, n. 9, p. 2832-2858, SEP 2009.
• Citações Web of Science: 3

Resumo

The dynamical discrete web (DyDW), introduced in the recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter tau. The evolution is by independent updating of the underlying Bernoulli variables indexed by discrete space-time that define the discrete web at any fixed tau. In this paper, we study the existence of exceptional (random) values of tau where the paths of the web do not behave like usual random walks and the Hausdorff dimension of the set of such exceptional tau. Our results are motivated by those about exceptional times for dynamical percolation in high dimension by Haggstrom, Peres and Steif, and in dimension two by Schramm and Steif. The exceptional behavior of the walks in the DyDW is rather different from the situation for the dynamical random walks of Benjamini, Haggstrom, Peres and Steif. For example, we prove that the walk from the origin S(0)(tau) violates the law of the iterated logarithm (LIL) on a set of tau of Hausdorff dimension one. We also discuss how these and other results should extend to the dynamical Brownian web, the natural scaling limit of the DyDW. (C) 2009 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 04/07276-2 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Luiz Renato Gonçalves Fontes
• Modalidade de apoio: Auxílio à Pesquisa - Temático