Radius and profile of random planar maps with faces of arbitrary degrees.
Random and deterministic perturbations of nonlinear oscillators.
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 dynamics and its applications.
Random ergodic theorems for sub-Markovian operators
Random evolutions processes induced by discrete time Markov chains.
Random fractals generated by a local Gaussian process indexed by a class of functions
In this paper, we extend the results of Orey and Taylor [S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc.28 (1974) 174–192] relative to random fractals generated by oscillations of Wiener processes to a multivariate framework. We consider a setup where Gaussian processes are indexed by classes of functions.
Random fractals generated by a local gaussian process indexed by a class of functions
In this paper, we extend the results of Orey and Taylor [S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? Proc. London Math. Soc. 28 (1974) 174–192] relative to random fractals generated by oscillations of Wiener processes to a multivariate framework. We consider a setup where Gaussian processes are indexed by classes of functions.
Random matrices, non-colliding processes and queues
Random paths with bounded local time
We consider one-dimensional Brownian motion conditioned (in a suitable sense) to have a local time at every point and at every moment bounded by some fixed constant. Our main result shows that a phenomenon of entropic repulsion occurs: that is, this process is ballistic and has an asymptotic velocity approximately 4.58... as high as required by the conditioning (the exact value of this constant involves the first zero of a Bessel function). We also study the random walk case and show that the process...
Random Phenomena and Some Systems Generating Words
Random processes with convex coordinates on triangular graphs.
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 recursive trees and the Bolthausen-Sznitman coalescent.
Random sampling of labeled tournaments.
Random split of the interval [0,1]
We define two splitting procedures of the interval [0,1], one using uniformly distributed points on the chosen piece and the other splitting a piece in half. We also define two procedures for choosing the piece to be split; one chooses a piece with a probability proportional to its length and the other chooses each piece with equal probability. We analyse the probability distribution of the lengths of the pieces arising from these procedures.
Random sums of random vectors and multitype families of productive individuals.
Random trees and applications.
Random variational inequalities in the absence of sample path continuity.
Random walk attracted by percolation clusters.