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A growth-fragmentation model connected to the ricocheted stable process

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  08 November 2022

Alexander R. Watson Open the ORCID record for Alexander R. Watson [Opens in a new window]
Alexander R. Watson*
Affiliation:
University College London
*
*Postal address: Gower Street, WC1E 6BT, UK. Email: [email protected]
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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.

Keywords

random planar mapsstatistical physicsLévy processstable processself-similar Markov process

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60G18: Self-similar processes
Secondary: 60G52: Stable processes 60G51: Processes with independent increments; L'evy processes
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 2 , June 2023 , pp. 493 - 503
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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