Ir al contenido

Documat


Sublogarithmic fluctuations for internal DLA

  • Amine Asselah [1] ; Alexandre Gaudillière [2]
    1. [1] Université Paris-Est
    2. [2] Université de Provence
  • Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 41, Nº. 3, 1, 2013, págs. 1160-1179
  • Idioma: inglés
  • DOI: 10.1214/11-AOP735
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. It is known that the asymptotic shape of the cluster is a sphere. When the dimension is two or more, we have shown in a previous paper that the inner (resp., outer) fluctuations of its radius is at most of order log(radius) [resp., log2(radius)]. Using the same approach, we improve the upper bound on the inner fluctuation to log(radius)−−−−−−−−−√ when d is larger than or equal to three. The inner fluctuation is then used to obtain a similar upper bound on the outer fluctuation.


Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno