2021/09/23 by Nathanaël Berestycki, Vittoria Silvestri, Berestycki, Nathanaël +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2109.11466
openalex publication_date 2021/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a constrained version of the HL(0) Hastings--Levitov model of aggregation in the complex plane, in which particles can only attach to the part of the cluster that has already been grown. Although one might expect that this gives rise to a non-trivial limiting shape, we prove that the cluster grows explosively: in the upper half plane, the aggregate accumulates infinite diameter as soon as it reaches positive capacity. More precisely, we show that after nt particles of (half-plane) capacity 1/(2n) have attached, the diameter of the shape is highly concentrated around √(tlog n), uniformly in t∈ [0,T]. This illustrates a new instability phenomenon for the growth of single trees/fjords in unconstrained HL(0).