On Diffusion Limited Deposition
Year: 2015
Type: preprint
Abstract: We propose a simple model of columnar growth through {\it diffusion limited aggregation} (DLA). Consider a graph $G_N\times\N$, where the basis has $N$ vertices $G_N:=\{1,\dots,N\}$, and two vertices $(x,h)$ and $(x',h')$ are adjacent if $|h-h'|\le 1$. Consider there a simple random walk {\it coming from infinity} which {\it deposits} on a growing cluster as follows: the cluster is a collection of columns, and the height of the column first hit by the walk immediately grows by one unit. Thus, columns do not grow laterally. We prove that there is a critical time scale $N/\log(N)$ for the maximal height of the piles, i.e., there exist constants $α
Source: arXiv (Cornell University)
Authors: Asselah, A., Cirillo, E., Scoppola, E., Scoppola, B.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W6947954265
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