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Internal diffusion limited aggregation on $$\mathbb{Z}'d$$. (Agrégation limitée par diffusion interne sur $$\mathbb Z^d$$.) (French) Zbl 1001.60051
P. Diaconis and W. Fulton [Rend. Semin. Mat., Torino 49, No. 1, 95-119 (1991; Zbl 0776.60128)] introduced a growth model on an infinite set associated with a Markov chain on that set. This model has been investigated for simple random walks on $$\mathbb{Z}^d$$, in particular, the limiting shape of the cloud of points has been found. The present author extends these results to the case of centered and irreducible random walks on $$\mathbb{Z}^d$$ under moment conditions. The non-centered case is also considered.

##### MSC:
 60G50 Sums of independent random variables; random walks
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