Growth-fragmentation processes model the evolution of positive masses which undergo binary divisions. The aim of this paper is twofold. First, we extend the theory of growth-fragmentation processes to allow signed mass. Among other things, we introduce genealogical martingales and establish a spinal decomposition for the associated cell system, following [BBCK18]. Then, we study a particular family of such self-similar signed growth-fragmentation processes which arise when cutting half-planar excursions at horizontal levels. When restricting this process to the positive masses in a special case, we recover part of the family introduced by Bertoin, Budd, Curien and Kortchemski in [BBCK18].
Supported by the FWF grant P33083 on “Scaling limits in random conformal geometry”.
I am grateful to Élie Aïdékon for suggesting me this project, and for his involvement and guidance all the way. I also thank Juan Carlos Pardo for stimulating discussions and for correcting some mistakes in a preliminary version of this paper, as well as Alex Watson for discussions about the change of measures in Section 6.7. I am grateful to Grégory Miermont for suggesting some important changes. After completing this work, I was informed that the link between growth-fragmentation processes and half-planar excursions was already predicted by Timothy Budd in an unpublished note. Finally, I want to thank an anonymous referee for their valuable comments and suggestions.
"Self-similar signed growth-fragmentations." Electron. J. Probab. 28 1 - 45, 2023. https://doi.org/10.1214/23-EJP937