9 papers · 1 filter
The largest common subtree of two random trees
Omer Angel, Caelan Atamanchuk, Anna Brandenberger +2
We study the size and structure of the largest common subtree (LCS) between two independent Bienaymé trees conditioned to have size . When the trees are critical with finite $2…
An elementary proof of the bunkbed conjecture for forests
Serte Donderwinkel, Joost Jorritsma, Guillem Perarnau
Although false for general graphs, this note gives an elementary proof of the bunkbed conjecture for any acyclic graph. The argument is short and self-contained, and may be of educ…
Evolution of recursive trees with limited memory
Omer Angel, Shankar Bhamidi, Serte Donderwinkel +2
Motivated by questions in social networks, distributed computing and probabilistic combinatorics, the last few years have seen increasing interest in network evolution models where…
Revisiting scaling limits for critical inhomogeneous random graphs with finite third moments
Louigi Addario-Berry, Sasha Bell, Prabhanka Deka +4
We consider the rank-1 inhomogeneous random graph in the Brownian regime in the critical window. Aldous studied the weights of the components, and showed that this ordered sequence…
Discrete snakes with globally centered displacements
Louigi Addario-Berry, Serte Donderwinkel, Christina Goldschmidt +1
We prove a scaling limit for globally centered discrete snakes on size-conditioned critical Bienaymé trees. More specifically, under a global finite variance condition, we prove c…
SinaÄ excursions: An analogue of Sparre Andersen's formula for the area process of a random walk
Serte Donderwinkel, Brett Kolesnik
SinaÄ initiated the study of random walks with persistently positive area processes, motivated by shock waves in solutions to the inviscid Burgers' equation. We find the precise a…