Diffusion limited aggregation on a tree

dc.creatorBarlow, MArtin T.
dc.creatorPemantle, Robin
dc.creatorPerkins, Edwin A.
dc.date2004-04-05
dc.date.accessioned2026-07-07T05:07:08Z
dc.date.available2026-07-07T05:07:08Z
dc.descriptionWe 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.description56 pages
dc.identifierhttps://arxiv.org/abs/math/0404089
dc.identifierhttp://arxiv.org/abs/math/0404089
dc.identifierProb. Th. Rel. Fields, 107, 1 - 60 (1997)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70738
dc.subjectProbability
dc.subject60K40, 60K30 (Primary) 60F05, 60F15, 60K35 (Secondary)
dc.titleDiffusion limited aggregation on a tree
dc.typetext

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