Stabilization of dla in a wedge

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Abstract

We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than µ/4, there is some a > 2 such that almost surely, for all Ra large enough, after time Ra all new particles attached to the DLA will be at distance larger than R from the origin. Furthermore, we provide estimates on the size of R under which this holds. This means that DLA stabilizes in growing balls, thus allowing a definition of the infinite DLA in a wedge via a finite time process.

Original languageEnglish
Article number42
JournalElectronic Journal of Probability
Volume25
DOIs
StatePublished - 2020

Keywords

  • Beurling estimate
  • Diffusion limited aggregation
  • Growth model
  • Harmonic measure
  • Reflected random walk
  • Stabilization

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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