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October, 1992 Internal Diffusion Limited Aggregation
Gregory F. Lawler, Maury Bramson, David Griffeath
Ann. Probab. 20(4): 2117-2140 (October, 1992). DOI: 10.1214/aop/1176989542


We study the asymptotic shape of the occupied region for an interacting lattice system proposed recently by Diaconis and Fulton. In this model particles are repeatedly dropped at the origin of the $d$-dimensional integers. Each successive particle then performs an independent simple random walk until it "sticks" at the first site not previously occupied. Our main theorem asserts that as the cluster of stuck particles grows, its shape approaches a Euclidean ball. The proof of this result involves Green's function asymptotics, duality and large deviation bounds. We also quantify the time scale of the model, establish close connections with a continuous-time variant and pose some challenging problems concerning more detailed aspects of the dynamics.


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Gregory F. Lawler. Maury Bramson. David Griffeath. "Internal Diffusion Limited Aggregation." Ann. Probab. 20 (4) 2117 - 2140, October, 1992.


Published: October, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0762.60096
MathSciNet: MR1188055
Digital Object Identifier: 10.1214/aop/1176989542

Primary: 60K35

Keywords: Diffusion limited aggregation , Growth model , Interacting particle system , Random walk

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 4 • October, 1992
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