# Rerooting multi-type branching trees: the infinite spine case

## TL;DR

This paper investigates the local convergence of rerooted conditioned multi-type Galton--Watson trees, revealing limit objects that depend on the types recurring infinitely often along the spine, extending Aldous's work to multitype cases.

## Contribution

It introduces new local convergence results for multitype Galton--Watson trees and characterizes the limit objects based on type recurrence along the spine.

## Key findings

- Limit objects are multitype variants of Aldous's sin-tree.
- Convergence results depend on types recurring infinitely often.
- Extends classical results to multitype branching processes.

## Abstract

We prove local convergence results of rerooted conditioned multi-type Galton--Watson trees. The limit objects are multitype variants of the random sin-tree constructed by Aldous (1991), and differ according to which types recur infinitely often along the backwards growing spine.

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Source: https://tomesphere.com/paper/1908.04843