A note on fluctuations for internal diffusion limited aggregation - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2010

A note on fluctuations for internal diffusion limited aggregation

Résumé

We consider a cluster growth model on Z^d, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It is known that the asymptotic shape of the cluster is spherical. Also, when dimension is 2 or more, and when the cluster has volume $n^d$, it is known that fluctuations of the radius are at most of order $n^{1/3}$. We improve this estimate to $n^{1/(d+1)}$, in dimension 3 or more. In so doing, we introduce a closely related cluster growth model, that we call the flashing process, whose fluctuations are controlled easily and accurately. This process is coupled to internal DLA to yield the desired bound. Part of our proof adapts the approach of Lawler, Bramson and Griffeath, on another space scale, and uses a sharp estimate (written by Blachere in our Appendix) on the expected time spent by a random walk inside an annulus.

Dates et versions

hal-00795850 , version 1 (01-03-2013)

Identifiants

Citer

Amine Asselah, Alexandre Gaudilliere. A note on fluctuations for internal diffusion limited aggregation. 2010. ⟨hal-00795850⟩
108 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More