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Internal Diffusion Limited Aggregation on Discrete Groups Having Exponential Growth
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  • Published: 07 June 2006

Internal Diffusion Limited Aggregation on Discrete Groups Having Exponential Growth

  • Sébastien Blachère1 &
  • Sara Brofferio2 

Probability Theory and Related Fields volume 137, pages 323–343 (2007)Cite this article

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Abstract

The internal diffusion limited aggregation (DLA) has been introduced by Diaconis and Fulton [Rend. Sem. Mat. Univ. Pol. Torino 49, 95–119 (1991)]. It is a growth model defined on an infinite set and associated to a Markov chain on this set. We focus here on sets which are finitely generated groups with exponential growth. We prove a shape theorem for the internal DLA on such groups associated to symmetric random walks. For that purpose, we introduce a new distance associated to the Green function, which happens to have some interesting properties. In the case of homogeneous trees, we also get the right order for the fluctuations of that model around its limiting shape.

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Author information

Authors and Affiliations

  1. CMI, Université Aix-Marseille 1, 39 rue Joliot-Curie, 13453, Marseille Cedex, France

    Sébastien Blachère

  2. Laboratoire de Mathématiques, Université Paris-Sud, bât. 425, 91405, Orsay Cedex, France

    Sara Brofferio

Authors
  1. Sébastien Blachère
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  2. Sara Brofferio
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Corresponding author

Correspondence to Sébastien Blachère.

Additional information

Sébastien Blachère’s research was supported by the ESF program ‘Phase transition and fluctuation phenomena for random dynamics in spatially extended systems’ ref. 554 and by Marie Curie Fellowship HPMF-CT-2002-02137. Sara Brofferio’s research was supported by Marie Curie Fellowship HPMF-CT-2002-02137.

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Blachère, S., Brofferio, S. Internal Diffusion Limited Aggregation on Discrete Groups Having Exponential Growth. Probab. Theory Relat. Fields 137, 323–343 (2007). https://doi.org/10.1007/s00440-006-0009-2

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  • Received: 28 July 2005

  • Revised: 20 March 2006

  • Published: 07 June 2006

  • Issue Date: March 2007

  • DOI: https://doi.org/10.1007/s00440-006-0009-2

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Keywords

  • Interacting particle systems
  • Random walks on groups
  • Green function

AMS Subject Classifications (2000)

  • 60B15
  • 60K35
  • 82B24
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