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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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