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On weighted U-statistics for stationary random fields

Jana Klicnarová (2017)

Kybernetika

The aim of this paper is to introduce a central limit theorem and an invariance principle for weighted U-statistics based on stationary random fields. Hsing and Wu (2004) in their paper introduced some asymptotic results for weighted U-statistics based on stationary processes. We show that it is possible also to extend their results for weighted U -statistics based on stationary random fields.

Perturbed Toeplitz operators and radial determinantal processes

Torsten Ehrhardt, Brian Rider (2013)

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

We study a class of rotation invariant determinantal ensembles in the complex plane; examples include the eigenvalues of Gaussian random matrices and the roots of certain families of random polynomials. The main result is a criterion for a central limit theorem to hold for angular statistics of the points. The proof exploits an exact formula relating the generating function of such statistics to the determinant of a perturbed Toeplitz matrix.

Physical measures for infinite-modal maps

Vítor Araújo, Maria José Pacifico (2009)

Fundamenta Mathematicae

We analyze certain parametrized families of one-dimensional maps with infinitely many critical points from the measure-theoretical point of view. We prove that such families have absolutely continuous invariant probability measures for a positive Lebesgue measure subset of parameters. Moreover, we show that both the density of such a measure and its entropy vary continuously with the parameter. In addition, we obtain exponential rate of mixing for these measures and also show that they satisfy the...

Planar Lorentz process in a random scenery

Françoise Pène (2009)

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

We consider the periodic planar Lorentz process with convex obstacles (and with finite horizon). In this model, a point particle moves freely with elastic reflection at the fixed convex obstacles. The random scenery is given by a sequence of independent, identically distributed, centered random variables with finite and non-null variance. To each obstacle, we associate one of these random variables. We suppose that each time the particle hits an obstacle, it wins the amount given by the random variable...

Poincaré Inequalities and Moment Maps

Bo’az Klartag (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in n . Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of p -spaces in n for 0 < p < 1 .

Pointwise ergodic theorems with rate and application to the CLT for Markov chains

Christophe Cuny, Michael Lin (2009)

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

Let T be Dunford–Schwartz operator on a probability space (Ω, μ). For f∈Lp(μ), p>1, we obtain growth conditions on ‖∑k=1nTkf‖p which imply that (1/n1/p)∑k=1nTkf→0 μ-a.e. In the particular case that p=2 and T is the isometry induced by a probability preserving transformation we get better results than in the general case; these are used to obtain a quenched central limit theorem for additive functionals of stationary ergodic Markov chains, which improves those of Derriennic–Lin and Wu–Woodroofe....

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