Diffusion limited aggregation on a tree
| dc.creator | Barlow, MArtin T. | |
| dc.creator | Pemantle, Robin | |
| dc.creator | Perkins, Edwin A. | |
| dc.date | 2004-04-05 | |
| dc.date.accessioned | 2026-07-07T05:07:08Z | |
| dc.date.available | 2026-07-07T05:07:08Z | |
| dc.description | We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to alpha^{-n}, where alpha<1 is a positive real parameter. The heights of these clusters are shown to increase linearly with their total size; this complements known results that show the height increases only logarithmically when alpha>=1. Results are obtained using stochastic monotonicity and regeneration results which may be of independent interest. Our motivation comes from two other ways in which the model may be viewed: as a problem in first-passage percolation, and as a version of diffusion-limited aggregation (DLA), adjusted so that `fingering' occurs. | |
| dc.description | 56 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404089 | |
| dc.identifier | http://arxiv.org/abs/math/0404089 | |
| dc.identifier | Prob. Th. Rel. Fields, 107, 1 - 60 (1997) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70738 | |
| dc.subject | Probability | |
| dc.subject | 60K40, 60K30 (Primary) 60F05, 60F15, 60K35 (Secondary) | |
| dc.title | Diffusion limited aggregation on a tree | |
| dc.type | text |