Radius and profile of random planar maps with faces of arbitrary degrees.
Random coefficients bifurcating autoregressive processes
This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton−Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new results in both these frameworks.
Random real trees
We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real trees called stable trees, which generalize the CRT. We review several important results concerning stable...
Random sums of random vectors and multitype families of productive individuals.
Random trees and applications.
Random Walks and Trees
These notes provide an elementary and self-contained introduction to branching random walks. Section 1 gives a brief overview of Galton–Watson trees, whereas Section 2 presents the classical law of large numbers for branching random walks. These two short sections are not exactly indispensable, but they introduce the idea of using size-biased trees, thus giving motivations and an avant-goût to the main part, Section 3, where branching random walks...
Random walks on Galton-Watson trees with infinite variance offspring distribution conditioned to survive.
Rate of growth of a transient cookie random walk.
Recurrence and transience of a multi-excited random walk on a regular tree.
Recurrence for branching Markov chains.
Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration
Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion
Restricted exchangeable partitions and embedding of associated hierarchies in continuum random trees
We introduce the notion of a restricted exchangeable partition of . We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In particular, we deduce from the general theory developed here a limit result conjectured previously for Ford’s alpha model and its extension, the alpha-gamma model, where restricted exchangeability arises naturally.
Riccati's differential equation in birth-death processes.
This note reviews the occurrence of Riccati's equation in three birth-death type processes, and outlines their solutions.
Robust Parametric Estimation of Branching Processes with a Random Number of Ancestors
2000 Mathematics Subject Classification: 60J80.The paper deals with a robust parametric estimation in branching processes {Zt(n)} having a random number of ancestors Z0(n) as both n and t tend to infinity (and thus Z0(n) in some sense). The offspring distribution is considered to belong to a discrete analogue of the exponential family – the class of the power series offspring distributions. Robust estimators, based on one and several sample paths, are proposed and studied for all values of the offspring...