Stationary DLA is Well Defined

Eviatar B. Procaccia, Jiayan Ye, Yuan Zhang

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper, we construct an infinite stationary diffusion limited aggregation (SDLA) on the upper half planar lattice, growing from an infinite line, with local growth rate proportional to the stationary harmonic measure. This model was suggested by Itai Benjamini. The main issue is a known problem in DLA models, the long range effects of large arms. In this paper we overcome this difficulty via a multi-scale argument controlling the dynamical discrepancies created on all scales while running two coupled SDLA on different starting configurations.

Original languageEnglish
Pages (from-to)1089-1111
Number of pages23
JournalJournal of Statistical Physics
Issue number4
StatePublished - 1 Nov 2020
Externally publishedYes


  • Diffusion limited aggregation
  • Interacting particle system
  • Stationary harmonic measure

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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