Journal of Statistical Physics

, Volume 131, Issue 6, pp 1185–1188 | Cite as

Exponential Clogging Time for a One Dimensional DLA

  • Itai Benjamini
  • Christopher Hoffman


In this paper a simple DLA type model is analyzed. In (Benjamini and Yadin in Commun. Math. Phys. 279:187–223, [2008]) the standard DLA model from (Witten and Sander in Phys. Rev. B 27:5686–5697, [1983]) was considered on a cylinder and the arm growing phenomena was established, provided that the section of the cylinder has sufficiently fast mixing rate. When considering DLA on a cylinder it is natural to ask how many particles it takes to clog the cylinder, e.g. modeling clogging of arteries. In this note we formulate a very simple DLA clogging model and establish an exponential lower bound on the number of particles arriving before clogging appears. In particular we possibly shed some light on why it takes so long to reach the bypass operation.


Growth process DLA Clogging 


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  1. 1.
    Benjamini, I., Yadin, A.: Diffusion limited aggregation on a cylinder. Commun. Math. Phys. 279, 187–223 (2008). arXiv:math/0701201 CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Witten, T., Sander, L.: Diffusion-limited aggregation. Phys. Rev. B 27, 5686–5697 (1983) CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsThe Weizmann InstituteRehovotIsrael
  2. 2.Department of MathematicsUniversity of WashingtonSeattleUSA

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