Scaling limits of random trees and planar maps

TL;DR

This paper reviews recent developments in the scaling limits of random trees and planar maps, focusing on their connections with bijective enumeration and Gromov-Hausdorff convergence, based on lecture notes from a summer school.

Contribution

It provides a comprehensive overview of the latest research on the scaling limits of random trees and planar maps, emphasizing their mathematical relationships and convergence properties.

Findings

Establishes connections between random trees, planar maps, and bijective enumeration.

Discusses Gromov-Hausdorff convergence in the context of scaling limits.

Summarizes recent advances presented in lecture notes from a summer school.

Abstract

These are the notes for a series of lectures given at the Clay Mathematical Institute Summer School in Buzios, July 11 - August 7, 2010. We review some of the recent aspects of scaling limits of random trees and planar maps, in particular via their relations with bijective enumeration and Gromov-Hausdorff convergence.