A growth-fragmentation model connected to the ricocheted stable process

TL;DR

This paper introduces a new growth-fragmentation process linked to random planar maps and the ricocheted stable process, with implications for planar Brownian motion and Liouville quantum gravity.

Contribution

It develops a novel growth-fragmentation model connected to the ricocheted stable process, expanding applications in statistical physics and quantum gravity.

Findings

Connects growth-fragmentation to random planar maps with large faces

Links the process to the ricocheted stable process

Applications to planar Brownian motion and Liouville quantum gravity

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.