A note on fluctuations for internal diffusion limited aggregation

• DOI: 10.48550/arxiv.1004.4665
• Publication Date: 2010-01-01
• Authors: Amine Asselah; Alexandre Gaudill...
• Keywords: Diffusion-limited aggregation

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