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Diffusion-limited aggregation on a tree
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  • Published: January 1997

Diffusion-limited aggregation on a tree

  • Martin T. Barlow1,
  • Robin Pemantle2 &
  • Edwin A. Perkins1 

Probability Theory and Related Fields volume 107, pages 1–60 (1997)Cite this article

  • 181 Accesses

  • 17 Citations

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Summary.

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 α −n, where α < 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 α≧ 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.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada (e-mail: barlow@math.ubc.ca) , , , , , , CA

    Martin T. Barlow & Edwin A. Perkins

  2. Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USA, , , , , , US

    Robin Pemantle

Authors
  1. Martin T. Barlow
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  2. Robin Pemantle
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  3. Edwin A. Perkins
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Additional information

Received: 16 August 1994 / In revised form: 18 March 1996

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Barlow, M., Pemantle, R. & Perkins, E. Diffusion-limited aggregation on a tree. Probab Theory Relat Fields 107, 1–60 (1997). https://doi.org/10.1007/s004400050076

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  • Issue Date: January 1997

  • DOI: https://doi.org/10.1007/s004400050076

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  • Mathematics Subject Classification (1991): 60K40
  • 60K30
  • 60K99
  • 60F05
  • 60F15
  • 60K35
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