For self-similar growth-fragmentations, the intrinsic area of small root-centered balls has a deterministic almost-sure rate with positive initial size and logarithmic fluctuations when the initial size is zero.
Markovian growth-fragmentation processes
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Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces
For self-similar growth-fragmentations, the intrinsic area of small root-centered balls has a deterministic almost-sure rate with positive initial size and logarithmic fluctuations when the initial size is zero.