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Teoría ergódica y simetrización.

Francesc Bofill (1982)

Stochastica

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

Grégory Miermont (2009)

Annales scientifiques de l'École Normale Supérieure

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

Gabriel Lang, Eric Marcon (2013)

ESAIM: Probability and Statistics

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...

The almost sure central limit theorems for certain order statistics of some stationary Gaussian sequences

Marcin Dudziński (2009)

Annales UMCS, Mathematica

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 brownian cactus I. Scaling limits of discrete cactuses

Nicolas Curien, Jean-François Le Gall, Grégory Miermont (2013)

Annales de l'I.H.P. Probabilités et statistiques

The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space E , one can associate an -tree called the continuous cactus of E . 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...

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