Teoría ergódica y simetrización.
We study the relations between simetrization by a limiting process of probabilities and functions defined on a metric compacy product space and their ergodic properties.
Tessellations of random maps of arbitrary genus
We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing one to encode such structures by labeled maps with a fixed number of faces. We investigate the scaling limits of the latter. Applications include asymptotic enumeration results for quadrangulations, and typical metric properties of randomly sampled quadrangulations. In particular, we show that scaling limits of these...
Testing randomness of spatial point patterns with the Ripley statistic
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness corresponding to a homogeneous Poisson point process. We first compute the exact first and second moment of the Ripley K-statistic under the homogeneous Poisson point process model. Then we prove the asymptotic normality of a vector of such statistics for different...
Testing the independence of two Poisson processes.
Tests for the presence of trends in linear processes [Book]
The law generalized for non-denumerable families of events and of -algebras of events
The Aizenman-Sims-Starr and Guerra's schemes for the SK model with multidimensional spins.
The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences
Suppose that X1, X2, … is some stationary zero mean Gaussian sequence with unit variance. Let {kn} be a certain nondecreasing sequence of positive integers, [...] denote the kn largest maximum of X1, … Xn. We aim at proving the almost sure central limit theorems for the suitably normalized sequence [...] under certain additional assumptions on {kn} and the covariance function [...]
The almost sure invariance principle for the empirical process of U-statistic structure
The analytic fixed point function. II.
The Arcsine law as the limit of the internal DLA cluster generated by Sinai’s walk
We identify the limit of the internal DLA cluster generated by Sinai’s walk as the law of a functional of a brownian motion which turns out to be a new interpretation of the Arcsine law.
The asymptotic distribution of the bootstrap sample mean of an infinitesimal array
The asymptotics of spherical functions and the central limit theorem on symmetric cones
We prove a central limit theorem for certain invariant random variables on the symmetric cone in a formally real Jordan algebra. This extends form the previous results of Richards and Terras on the cone of real positive definite matrices.
The Barnes G function and its relations with sums and products of generalized gamma convolution variables.
The Berry-Esseen Bound for Minimum Contrast Estimators in the Independent not Identically Distributed Case.
The Berry-Esseen theorem for rank statistics
The best constant in the Khintchine inequality for complex Steinhaus variables, the case p=1
The Beurling estimate for a class of random walks.
The bootstrap of the mean with arbitrary bootstrap sample size
The brownian cactus I. Scaling limits of discrete cactuses
The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space , one can associate an -tree called the continuous cactus of . We prove under general assumptions that the cactus of random planar maps distributed according to Boltzmann weights and conditioned to have a fixed large number of vertices converges in distribution to a limiting space called the Brownian cactus, in the Gromov–Hausdorff sense. Moreover, the Brownian cactus...