Results 1 
8 of
8
Gibbs distributions for random partitions generated by a fragmentation process
, 2006
"... process ..."
Ranked fragmentations
 ESAIM P&S
"... distributions for random partitions generated by a ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
(Show Context)
distributions for random partitions generated by a
Distances between pairs of vertices and Vertical Profile in conditioned GaltonWatson trees
, 2009
"... We consider a conditioned Galton–Watson tree and prove an estimate of the number of pairs of vertices with a given distance, or, equivalently, the number of paths of a given length. We give two proofs of this result, one probabilistic and the other using generating functions and singularity analysi ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
(Show Context)
We consider a conditioned Galton–Watson tree and prove an estimate of the number of pairs of vertices with a given distance, or, equivalently, the number of paths of a given length. We give two proofs of this result, one probabilistic and the other using generating functions and singularity analysis. Moreover, the latter proof yields a more general estimate for generating functions, which is used to prove a conjecture by Bousquet–Mélou and Janson [5], saying that the vertical profile of a randomly labelled conditioned Galton–Watson tree converges in distribution, after suitable normalization, to the density of ISE (Integrated Superbrownian Excursion).
SUBGAUSSIAN TAIL BOUNDS FOR THE WIDTH AND HEIGHT OF CONDITIONED GALTON–WATSON TREES.
, 2010
"... We study the height and width of a Galton–Watson tree with offspring distribution ξ satisfying E ξ = 1, 0 < Var ξ < ∞, conditioned on having exactly n nodes. Under this conditioning, we derive subGaussian tail bounds for both the width (largest number of nodes in any level) and height (greate ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
(Show Context)
We study the height and width of a Galton–Watson tree with offspring distribution ξ satisfying E ξ = 1, 0 < Var ξ < ∞, conditioned on having exactly n nodes. Under this conditioning, we derive subGaussian tail bounds for both the width (largest number of nodes in any level) and height (greatest level containing a node); the bounds are optimal up to constant factors in the exponent. Under the same conditioning, we also derive essentially optimal upper tail bounds for the number of nodes at level k, for 1 ≤ k ≤ n.
The height of increasing trees
, 2007
"... We extend results about heights of random trees (Devroye, 1986, 1987, 1998b). In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The height of these trees is shown to be in probability asymptotic to c log n for some consta ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We extend results about heights of random trees (Devroye, 1986, 1987, 1998b). In this paper, a general split tree model is considered in which the normalized subtree sizes of nodes converge in distribution. The height of these trees is shown to be in probability asymptotic to c log n for some constant c. We apply our results to obtain a law of large numbers for the height of all polynomial varieties of increasing trees (Bergeron et al., 1992).