One-dimensional long-range diffusion-limited aggregation III - The limit aggregate

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


In this paper we study the structure of the limit aggregate A∞ = ∪ N≥0 An of the one-dimensional long range diffusion limited aggregation process defined in (Ann. Probab. 44 (2016) 3546-3579). We show (under some regularity conditions) that for walks with finite third moment A∞ has renewal structure and positive density, while for walks with finite variance the renewal structure no longer exists and A∞ has 0 density. We define a tree structure on the aggregates and show some results on the degrees and number of ends of these random trees. We introduce a new "harmonic competition" model where different colours compete for harmonic measure, and show how the tree structure is related to coexistence in this model.

Original languageEnglish
Pages (from-to)1513-1527
Number of pages15
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number4
StatePublished - Nov 2017

Bibliographical note

Publisher Copyright:
© Association des Publications de l'Institut Henri Poincaré, 2017.


1Supported by the Israel Science Foundation (Grant No. 1471) and by a Grant from the GIF, the German-Israeli Foundation for Scientific Research and Development.

FundersFunder number
German-Israeli Foundation for Scientific Research and Development
Israel Science Foundation1471


    • DLA
    • Diffusion limited aggregation
    • Harmonic measure
    • Phase transition
    • Random walk
    • Renewal structure


    Dive into the research topics of 'One-dimensional long-range diffusion-limited aggregation III - The limit aggregate'. Together they form a unique fingerprint.

    Cite this