5 papers
Rare subtree patterns in size-conditioned Bienaymé trees: Poisson approximation and declumping
Igor Kortchemski, Leonard Vetter
We establish a general Poisson approximation for rare local patterns in critical Bienaymé--Galton--Watson trees with offspring distribution in the domain of attraction of a s…
Does freezing impede the growth of random recursive trees?
Anna Brandenberger, Simon Briend, Hannah Cairns +2
Uniform attachment with freezing is an extension of the classical model of random recursive trees, in which trees are recursively built by attaching new vertices to old ones. In th…
Condensation in subcritical Cauchy Bienaymé trees
Igor Kortchemski, Leonard Vetter
The goal of this note is to study the geometry of large size-conditioned Bienaymé trees whose offspring distribution is subcritical, belongs to the domain of attraction of a stabl…
The height of the infection tree
Emmanuel Kammerer, Igor Kortchemski, Delphin Sénizergues
We are interested in the geometry of the ``infection tree'' in a stochastic SIR (Susceptible-Infectious-Recovered) model, starting with a single infectious individual. This tree is…
Critical trees are neither too short nor too fat
Louigi Addario-Berry, Serte Donderwinkel, Igor Kortchemski
We establish lower tail bounds for the height, and upper tail bounds for the width, of critical size-conditioned Bienaymé trees. Our bounds are optimal at this level of generality…