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- Nicolas Broutin, Luc Devroye
- Algorithmica
- 2006

We use large deviations to prove a general theorem on the asymptotic edge-weighted height Hn* of a large class of random trees for which Hn* ∼ c log n for some positive constant c. A graphical… (More)

We consider the Erdős–Rényi random graph G(n, p) inside the critical window, that is when p = 1/n+ λn−4/3, for some fixed λ ∈ R. We prove that the sequence of connected components of G(n, p),… (More)

We consider a branching random walk for which the maximum position of a particle in the n’th generation, Rn, has zero speed on the linear scale: Rn/n → 0 as n → ∞. We further remove (“kill”) any… (More)

- Nicolas Broutin, Luc Devroye, Erin McLeish, M. de la Salle
- Random Struct. Algorithms
- 2008

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… (More)

Tries are data structures used to manipulate and store strings by taking advantage of the digital character of words. They were introduced by de la Briandais (1959). Apparently, the term of trie was… (More)

We provide simplified proofs for the asymptotic distribution of the number of cuts required to cut down a Galton–Watson tree with critical, finite-variance offspring distribution, conditioned to have… (More)

This extended abstract is dedicated to the analysis of the height of non-plane unlabelled rooted binary trees. The height of such a tree chosen uniformly among those of size n is proved to have a… (More)

We study a class of hypothesis testing problems in which, upon observing the realization of an n-dimensional Gaussian vector, one has to decide whether the vector was drawn from a standard normal… (More)

- Nicolas Broutin, Philippe Flajolet
- Random Struct. Algorithms
- 2012

This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees (“Otter trees”), when trees of a given size are taken with equal likelihood. The height… (More)

- Nicolas Broutin, Luc Devroye
- Combinatorics, Probability & Computing
- 2008

We analyze the weighted height of random tries built from independent strings of i.i.d. symbols on the finite alphabet {1, . . . , d}. The edges receive random weights whose distribution depends upon… (More)