Electronic Communications in Probability

Internal Diffusion-Limited Aggregation on non-amenable graphs

Wilfried Huss

Full-text: Open access


The stochastic growth model Internal Diffusion Limited Aggregation was defined in 1991 by Diaconis and Fulton. Several shape results are known when the underlying state space is the d-dimensional lattice, or a discrete group with exponential growth. We prove an extension of the shape result of Blachere and Brofferio for Internal Diffusion Limited Aggregation on a wide class of Markov chains on non-amenable graphs.

Article information

Electron. Commun. Probab., Volume 13 (2008), paper no. 27, 272-279.

Accepted: 25 May 2008
First available in Project Euclid: 6 June 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82B24: Interface problems; diffusion-limited aggregation 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

interacting particle systems random walks on graphs

This work is licensed under aCreative Commons Attribution 3.0 License.


Huss, Wilfried. Internal Diffusion-Limited Aggregation on non-amenable graphs. Electron. Commun. Probab. 13 (2008), paper no. 27, 272--279. doi:10.1214/ECP.v13-1374. https://projecteuclid.org/euclid.ecp/1465233454

Export citation


  • Diaconis, P.; Fulton, W. A growth model, a game, an algebra, Lagrange inversion, and characteristic classes. Commutative algebra and algebraic geometry, II (Italian) (Turin, 1990). Rend. Sem. Mat. Univ. Politec. Torino 49 (1991), no. 1, 95–119 (1993).
  • Lawler, Gregory F.; Bramson, Maury; Griffeath, David. Internal diffusion limited aggregation. Ann. Probab. 20 (1992), no. 4, 2117–2140.
  • Lawler, Gregory F. Subdiffusive fluctuations for internal diffusion limited aggregation. Ann. Probab. 23 (1995), no. 1, 71–86.
  • Blachère, Sébastien. Agrégation limitée par diffusion interne et temps de coupure sur les groupes discrets à croissance polynomiale. PhD thesis, L'Universitée Paul Sabatier, 2000.
  • Blachère, Sébastien. Internal diffusion limited aggregation on discrete groups having polynomial growth. In Random Walks and Geometry, Proceedings (Erwin Schroedinger Insitute, Vienna 2001). de Gruyter, Berlin, 2004.
  • Blachère, Sébastien; Brofferio, Sara. Internal diffusion limited aggregation on discrete groups having exponential growth. Probab. Theory Related Fields 137 (2007), no. 3-4, 323–343.
  • Blachère, S; Haïssinsky, P; Mathieu, P. Asymptotic entropy and Green speed for random walks on countable groups. Ann. Probab. 36 (2008) n.3 1134–1152.
  • Woess, Wolfgang. Random walks on infinite graphs and groups. Cambridge Tracts in Mathematics, 138. Cambridge University Press, Cambridge, 2000. xii+334 pp. ISBN: 0-521-55292-3
  • Dodziuk, Jozef. Difference equations, isoperimetric inequality and transience of certain random walks. Trans. Amer. Math. Soc. 284 (1984), no. 2, 787–794.
  • Dodziuk, J.; Kendall, W. S. Combinatorial Laplacians and isoperimetric inequality. From local times to global geometry, control and physics (Coventry, 1984/85), 68–74, Pitman Res. Notes Math. Ser., 150, Longman Sci. Tech., Harlow, 1986.