An introduction to the convergence of random trees.
Abstract
In this talk, we aim to present two notions of convergence of random trees through theory and examples, based on the approach taken in Le Gall's survey "Random trees and applications". The first is the convergence of contour and height functions of trees related to critical, non-degenerate Galton–Watson trees with finite variance. The second is an introduction to the class of metric spaces known as real trees, their encoding by continuous excursions, and the Gromov–Hausdorff distance between metric spaces.