7 papers · 1 filter
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…
Uniform integrability of the distance to the nearest leaf in random trees
VÃctor 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…
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…
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…
The scaling limit of random 2-connected series-parallel maps
Daniel Amankwah, Jakob Björnberg, Sigurdur Ãrn 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…
Limits of chordal graphs with bounded tree-width
Jordi CastellvÃ, Benedikt Stufler
We study random -connected chordal graphs with bounded tree-width. Our main results are scaling limits and quenched local limits.