The Scaling Limit of Random Two-Connected Series-Parallel Maps.

Authors

Daniel Amankwah, Jakob Björnberg, Sigurdur Örn Stefánsson, Benedikt Stufler, Joonas Turunen

Published in

Journal of theoretical probability. Volume 39. Issue 4. Pages 75. Epub Aug 27, 2026.

Abstract

A finite graph embedded in the plane is called a series-parallel map if it can be obtained from a finite tree by repeatedly subdividing and doubling edges. We study the scaling limit of weighted random two-connected series-parallel maps with n edges and show that under fairly general integrability conditions on these weights, the maps with distances rescaled by a factor $n^{-1/2}$ converge to a constant multiple of Aldous' continuum random tree (CRT) in the Gromov-Hausdorff sense. The proof relies on a bijection between a set of trees with n leaves and a set of series-parallel maps with n edges, together with a novel blob decomposition of the maps.

PMID:
42666367
Bibliographic data and abstract were imported from PubMed on 29 Aug 2026.

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