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Uniqueness and approximate computation of optimal incomplete transportation plans

P. C. Álvarez-Esteban, E. del Barrio, J. A. Cuesta-Albertos, C. Matrán (2011)

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

For α∈(0, 1) an α-trimming, P∗, of a probability P is a new probability obtained by re-weighting the probability of any Borel set, B, according to a positive weight function, f≤1/(1−α), in the way P∗(B)=∫Bf(x)P(dx). If P, Q are probability measures on euclidean space, we consider the problem of obtaining the best L2-Wasserstein approximation between: (a) a fixed probability and trimmed versions of the other; (b) trimmed versions of both probabilities. These best trimmed approximations naturally...

Universality in the bulk of the spectrum for complex sample covariance matrices

Sandrine Péché (2012)

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

We consider complex sample covariance matrices MN = (1/N)YY* where Y is a N × p random matrix with i.i.d. entries Yij, 1 ≤ i ≤ N, 1 ≤ j ≤ p, with distribution F. Under some regularity and decay assumptions on F, we prove universality of some local eigenvalue statistics in the bulk of the spectrum in the limit where N → ∞ and limN→∞ p/N = γ for any real number γ ∈ (0, ∞).

Vers un théorème de Skorohod simultané

Henri Heinich (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

Nous étudions un théorème de Skorohod pour des mesures vectorielles à valeurs ℝ d . En notant X ( ℙ ) la mesure image de ℙ par la variable aléatoire X , nous donnons des classes de mesures ℙ et éventuel-lement de variables telles que, si la suite { X n ( ℙ ) } converge étroitement, il existe une suite { φ n } , φ n ( ℙ ) = X n ( ℙ ) qui converge en mesure, éventuel-lement p.s.Le problème de Monge est abordé comme application. Soit | ℙ | la mesure variation de ℙ , pour un couple ( ℙ , ℚ ) et une fonction coût c , le problème de Monge est l’existence d’une fonction...

Weak Hölder convergence of processes with application to the perturbed empirical process

Djamel Hamadouche, Charles Suquet (1999)

Applicationes Mathematicae

We consider stochastic processes as random elements in some spaces of Hölder functions vanishing at infinity. The corresponding scale of spaces C 0 α , 0 is shown to be isomorphic to some scale of Banach sequence spaces. This enables us to obtain some tightness criterion in these spaces. As an application, we prove the weak Hölder convergence of the convolution-smoothed empirical process of an i.i.d. sample ( X 1 , . . . , X n ) under a natural assumption about the regularity of the marginal distribution function F of the...

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