Random laminations and multitype branching processes

TL;DR

This paper studies multitype branching processes related to random laminations of the disk, classifying their criticality and providing estimates using advanced mathematical theories.

Contribution

It introduces a classification of these processes and applies infinite dimensional Perron-Frobenius theory and quasi-stationary distributions to analyze their behavior.

Findings

Classification of processes as subcritical or supercritical

Kolmogorov-type estimates in the critical case

Application of infinite dimensional Perron-Frobenius theory

Abstract

We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical case corresponding to the random recursive lamination process of [1]. The proofs use the infinite dimensional Perron-Frobenius theory and quasi-stationary distributions.