of the mass of a typical ball in the Brownian map is refined, and we obtain a lower bound as well.

    **Keywords:** Self-similar growth-fragmentations; intrinsic area; rate of growth.

    **AMS MSC 2010:** 60J25; 60G18; 60G57.
author:
- 'François G. Ged[^1]'
bibliography:
- 'biblio.bib'
title: 'Intrinsic area near the origin for self-similar growth-fragmentations and related random surfaces'
---

Introduction
============

Growth-fragmentation processes form a family of continuous time branching processes that have been introduced by Bertoin [@B17]. They model particle systems without interaction where each particle is described by a positive real number that corresponds to its mass (or size), evolving by growing and splitting, with rates that can depend on its current mass. Note that these processes differ from (pure) fragmentation processes [@B01; @B04], for which growth is not allowed. The fragmentations are binary and when a particle splits, its mass is instantaneously randomly distributed among the two resulting fragments. A *self-similar growth-fragmentation* $(\mathbf{X}(t))_{t\geq 0}$ is a growth-fragmentation where every particle evolves according to a driving self-similar Markov process. Self-similarity refers to the property that the evolution of a particle of size $x>0$ is a scaling transformation of that of a particle of unit size, depending on some index $\alpha\in\mathbb{R}$. 