Radius and profile of random planar maps with faces of arbitrary degrees.
Random dynamics and its applications.
Random evolutions processes induced by discrete time Markov chains.
Random matrices and -theory for exact -algebras.
Random -ary sequence and mapping uniformly distributed
Višek [3] and Culpin [1] investigated infinite binary sequence with taking values or at random. They investigated also real mappings which have the uniform distribution on (notation ). The problem for -ary sequences is dealt with in this paper.
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 sets and their asymptotic measure
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 sum Limit Theorems for Nonidentically Distributed Random Variables
Random Sums Of Random Vectors
Random time changes for sock-sorting and other stochastic process limit theorems.
Random walk local time approximated by a brownian sheet combined with an independent brownian motion
Let ξ(k, n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process ξ(k, n)−ξ(0, n) in terms of a brownian sheet and an independent Wiener process (brownian motion), time changed by an independent brownian local time. Some related results and consequences are also established.
Random Walks in Attractive Potentials: The Case of Critical Drifts
We consider random walks in attractive potentials - sub-additive functions of their local times. An application of a drift to such random walks leads to a phase transition: If the drift is small than the walk is still sub-ballistic, whereas the walk is ballistic if the drift is strong enough. The set of sub-critical drifts is convex with non-empty interior and can be described in terms of Lyapunov exponents (Sznitman, Zerner ). Recently it was shown that super-critical drifts lead to a limiting...
Randomly Weighted Series of Contractions in Hilbert Spaces.
Rare events and conditional events on random strings.
Rate of convergence for a class of RCA estimators
This work deals with Random Coefficient Autoregressive models where the error process is a martingale difference sequence. A class of estimators of unknown parameter is employed. This class was originally proposed by Schick and it covers both least squares estimator and maximum likelihood estimator for instance. Asymptotic behavior of such estimators is explored, especially the rate of convergence to normal distribution is established.
Rate of convergence for large coupling limits by brownian motion
Rate of Convergence in the Central Limit Theorem and in the Strong Law of Large Numbers for von Mises Statistics.
Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long-range dependence.