{"paper":{"title":"On Diffusion Limited Deposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Asselah, B. Scoppola, E. Cirillo, E. Scoppola","submitted_at":"2015-05-14T21:24:43Z","abstract_excerpt":"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.\n  We prove that there is a critical time scale $N/\\log(N)$ for the maxi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03892","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}