A concentration inequality for the maximum vertex degree in random dissections

TL;DR

This paper establishes a concentration inequality for the maximum vertex degree in random polygon dissections, confirming a conjecture and utilizing bijections with dual trees and analytic combinatorics techniques.

Contribution

It provides the first proven concentration inequality for maximum vertex degree in random dissections, resolving a long-standing conjecture.

Findings

Proves a concentration inequality for maximum vertex degree

Uses bijection with dual trees and analytic combinatorics

Confirms a conjecture from 2012

Abstract

We obtain a concentration inequality for the maximum degree of a vertex in a uniformly random dissection of a polygon. This resolves a conjecture posed by Curien and Kortchemski in 2012. Our approach is based on a bijection with dual trees and the tools of analytic combinatorics.