Internal diffusion limited aggregation on \(\mathbb{Z}'d\). (Agrégation limitée par diffusion interne sur \(\mathbb Z^d\).) (French) Zbl 1001.60051

Blachère, Sébastien

Ann. Inst. Henri Poincaré, Probab. Stat. 38, No. 4, 613-648 (2002).

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.

Reviewer: Allan Gut (Uppsala)

MSC:

60G50

Sums of independent random variables; random walks