A growth-fragmentation model connected to the ricocheted stable process. (English) Zbl 1512.60058
Summary: Growth-fragmentation processes describe the evolution of systems in which cells grow slowly and fragment suddenly. Despite originating as a way to describe biological phenomena, they have recently been found to describe the lengths of certain curves in statistical physics models. In this note, we describe a new growth-fragmentation process connected to random planar maps with faces of large degree, having as a key ingredient the ricocheted stable process recently discovered by Budd. The process has applications to the excursions of planar Brownian motion and Liouville quantum gravity.
MSC:
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60G18 | Self-similar stochastic processes |
| 60G52 | Stable stochastic processes |
| 60G51 | Processes with independent increments; Lévy processes |
| 82D20 | Statistical mechanics of solids |
| 82M60 | Stochastic analysis in statistical mechanics |
Keywords:
random planar maps; statistical physics; Lévy process; stable process; self-similar Markov process; growth-fragmentation processReferences:
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