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arXiv · 1904.10168

On outer fluctuations for internal DLA

Amine Asselah·Alexandre Gaudillière
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Abstract

We had established inner and outer fluctuation for the internal DLA cluster when all walks are launched from the origin. In obtaining the outer fluctuation, we had used a deep lemma of Jerison, Levine and Sheffield, which estimate roughly the possibility of fingering, and had provided a simple proof using an interesting estimate for crossing probability for a simple random walk. The application of the crossing probability to the fingering for the internal DLA cluster contains a flaw discovered recently, that we correct in this note. We take the opportunity to make a self-contained exposition.

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Amine Asselah, Alexandre Gaudillière. 2019-04-23. On outer fluctuations for internal DLA. https://arxiv.org/abs/1904.10168

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