Author

Benedikt Stufler

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Open access Aug 2026

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

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 w...

Daniel Amankwah, J. Björnberg, Sigurdur Orn Stef'ansson et al. · Journal of theoretical proba... · 0 citations

Preprint Aug 2026

Non-bijective scaling limits and phase transitions of planar maps

We prove that the uniform random non-separable planar map with $n$ edges admits the Brownian sphere as Gromov--Hausdorff--Prokhorov scaling limit as $n$ tends to infinity. Our proof introduces a non-bijective ``common-core transfer method''that constitutes a novel and universal proof strategy for scaling limits of rand...

Benedikt Stufler · 0 citations

Preprint Jul 2026

Limit laws of random simplex tree-child networks

We prove that the longer and shorter Sackin indices of a uniformly random simplex tree-child network with $n$ taxa admit joint distributional limits after rescaling by $n^{-7/4}$. The limiting distributions are described by functionals of a Brownian excursion. We also identify the limiting law of the height after resca...

V'ictor J. Maci'a, Benedikt Stufler · 0 citations