Mathematical seminar with Daniel Amankwah - HÍ

10-4-2025 in room 157, VR-II

Speaker: Daniel Amankwah - HÍ

Title: Scaling Limits of Random Series-Parallel Maps.

Abstract: A finite graph embedded in the plane is called a series-parallel map if it can be constructed from a tree by iteratively subdividing and doubling edges. In this talk, we investigate the scaling limits of weighted random two-connected series-parallel maps with $n$ edges. Under suitable integrability conditions on the weights, we show that when distances are rescaled by a factor of $n^{-1/2}$, these maps converge in the Gromov--Hausdorff sense to a constant multiple of Aldous' continuum random tree (CRT). The proof relies on a bijection between certain families of trees and series-parallel maps, allowing us to analyze geodesics using a Markov chain argument introduced by Curien, Haas, and Kortchemski (2015).