20 citations · 44 across the 24 of their papers we have counts for
42 papers
Non-bijective scaling limits and phase transitions of planar maps
Benedikt Stufler
We prove that the uniform random non-separable planar map with edges admits the Brownian sphere as Gromov--Hausdorff--Prokhorov scaling limit as tends to infinity. Our proo…
Limit laws of random simplex tree-child networks
Víctor J. Maciá, Benedikt Stufler
We prove that the longer and shorter Sackin indices of a uniformly random simplex tree-child network with taxa admit joint distributional limits after rescaling by .…
Linear time sampling of Pólya trees
Benedikt Stufler
We present an algorithm for exact-size sampling of uniformly random Pólya trees with linear expected runtime.
Asymptotic enumeration of unlabelled cubic planar graphs
Benedikt Stufler
We determine the precise asymptotic number of unlabelled cubic planar graphs with vertices. Our approach blends generating series methods with computational bounds and probabil…
Uniform integrability of the distance to the nearest leaf in random trees
Víctor J. Maciá, Benedikt Stufler
We study the distance from the root to the nearest leaf, the analogous quantity for a uniformly chosen vertex, and its protection number, in size-conditioned simply generated trees…
Poisson-Dirichlet graphons and permutons
Benedikt Stufler
We introduce classes of supergraphs and superpermutations with novel universal graphon and permuton limiting objects whose construction involves the two-parameter Poisson-Dirichlet…
Scaling limits of multitype Bienaymé trees
Louigi Addario-Berry, Philipp Beltran, Benedikt Stufler +1
We consider critical multitype Bienaymé trees that are either irreducible or possess a critical irreducible component with attached subcritical components. These trees are studied…
The scaling limit of random 2-connected series-parallel maps
Daniel Amankwah, Jakob Björnberg, Sigurdur Örn Stefánsson +2
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 lim…
Gibbs partitions and lattice paths
Niccolò Bosio, Markus Kuba, Benedikt Stufler
This work is devoted to the analysis of a Gibbs partition model, also known as a composition scheme. We consider a natural new condition on the component weights. It leads to a new…
Limits of chordal graphs with bounded tree-width
Jordi Castellví, Benedikt Stufler
We study random -connected chordal graphs with bounded tree-width. Our main results are scaling limits and quenched local limits.
Poisson-Dirichlet scaling limits of Kemp's supertrees
Benedikt Stufler
We determine the Gromov--Hausdorff--Prokhorov scaling limits and local limits of Kemp's -dimensional binary trees and other models of supertrees. The limits exhibit a root verte…
Probabilistic enumeration and equivalence of nonisomorphic trees
Benedikt Stufler
We present a new probabilistic proof of Otter's asymptotic formula for the number of unlabelled trees with a given number of vertices. We additionally prove a new approximation res…
Decorated stable trees
Delphin Sénizergues, Sigurdur Örn Stefánsson, Benedikt Stufler
We define decorated -stable trees which are informally obtained from an -stable tree by blowing up its branchpoints into random metric spaces. This generalizes the -stable…
Gibbs partitions: a comprehensive phase diagram
Benedikt Stufler
We study Gibbs partition models, also known as composition schemes. Our main results comprehensively describe their phase diagram, including a phase transition from the convergent…
The scaling limit of random cubic planar graphs
Benedikt Stufler
We study the random simple connected cubic planar graph with an even number of vertices. We show that the Brownian map arises as Gromov--Hausdorff--Prokhorov sca…
First-passage percolation on random simple triangulations
Benedikt Stufler
We study first-passage percolation on random simple triangulations and their dual maps with independent identically distributed link weights. Our main result shows that the first-p…
The Uniform Infinite Cubic Planar Graph
Benedikt Stufler
We prove that the random simple cubic planar graph with an even number of vertices admits a novel uniform infinite cubic planar graph (UICPG) as quenched local l…
Mass and radius of balls in Gromov-Hausdorff-Prokhorov convergent sequences
Benedikt Stufler
We survey some properties of Gromov--Hausdorff--Prokhorov convergent sequences of random compact metric spaces equipp…
Exact-size Sampling of Enriched Trees in Linear Time
Konstantinos Panagiotou, Leon Ramzews, Benedikt Stufler
Various combinatorial classes such as outerplanar graphs and maps, series-parallel graphs, substitution-closed classes of permutations and many more allow bijective encodings by so…
Cut Vertices in Random Planar Maps
Michael Drmota, Marc Noy, Benedikt Stufler
The main goal of this paper is to determine the asymptotic behavior of the number of cut-vertices in random planar maps with edges. It is shown that in prob…
Quenched local convergence of Boltzmann planar maps
Benedikt Stufler
Stephenson~(2018) established annealed local convergence of Boltzmann planar maps conditioned to be large. The present work uses results on rerooted multi-type branching trees to p…
A branching process approach to level- phylogenetic networks
Benedikt Stufler
The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In the present work we introduce…
Local convergence of random planar graphs
Benedikt Stufler
The present work describes the asymptotic local shape of a graph drawn uniformly at random from all connected simple planar graphs with n labelled vertices. We establish a novel un…
Rerooting multi-type branching trees: the infinite spine case
Benedikt Stufler
We prove local convergence results of rerooted conditioned multi-type Galton--Watson trees. The limit objects are multitype variants of the random sin-tree constructed by Aldous (1…