A growth-fragmentation model connected to the ricocheted stable process

Abstract

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.

14 pages. v5 makes minor amendments

References in corpus (2)

• Infinitely ramified point measures and branching Lévy processes
• The peeling process on random planar maps coupled to an O(n) loop model (with an appendix by Linxiao Chen)