On outer fluctuations for internal DLA

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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Contributor : Alexandre Gaudilliere <>
Submitted on : Thursday, November 28, 2019 - 5:13:48 PM
Last modification on : Friday, November 29, 2019 - 2:31:00 AM

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  • HAL Id : hal-02385311, version 1
  • ARXIV : 1904.10168


Amine Asselah, Alexandre Gaudilliere. On outer fluctuations for internal DLA. 2019. ⟨hal-02385311⟩



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