Strong approximation results for the empirical process of stationary sequences

We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the empirical process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than $n^{-1-\delta}$ for some positive $\delta$. This shows that our conditions are in some sense optimal.Comment: Published in at http://dx.doi.org/10.1214/12-AOP798 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stability of Big Surface Bubbles: Impact of Evaporation and Bubbles Size

Surface bubbles have attracted much interest in the past decades. In this article, we propose to explore the lifetime and thinning dynamics of centimetric surface bubbles. We study the impact of the bubbles size as well as that of the atmospheric humidity through a careful control and systematic variation of the relative humidity in the measuring chamber. We first adress the question of the drainage under saturated water vapor conditions and show that a model including both capillary and gravity driven drainage provides the best prediction for this process. Additionally, unprecedented statistics on the bubbles lifetimes confirm experimentally that this parameter is set by evaporation to leading order. We make use of a model based on the overall thinning dynamics of the thin film and assume a rupture thickness of the order 10-100 nm to obtain a good representation of these data. For experiments conducted far from saturation, the convective evaporation of the bath is shown to dominate the overall mass loss in the cap film due to evaporation

A Bernstein type inequality and moderate deviations for weakly dependent sequences

In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviations results. Applications include classes of Markov chains, functions of linear processes with absolutely regular innovations and ARCH model

The Life of a Surface Bubble

Surface bubbles are present in many industrial processes and in nature, as well as in CO$_2$ beverage. They have motivated many theoretical, numerical and experimental works. This paper presents the current knowledge on the physics of surface bubbles lifetime and shows the diversity of mechanisms at play that depend on the properties of the bath, the interfaces and the ambient air. In particular, we explore the role of drainage and evaporation on film thinning. We highlight the existence of two different scenarios depending on whether the film cap ruptures at large or small thickness compared to the thickness at which van der Waals interaction come in to play

Legendre Bertrand : Ce que le numérique fait aux livres

Les ouvrages scientifiques sur le livre et le numérique ne sont pas nombreux et l’on comprend pourquoi tant il est souvent difficile de figer des réflexions sur un objet mouvant, longtemps considéré comme « en construction » et depuis peu en « déconstruction ». Mais cette entreprise est utile et avec cet ouvrage de 138 pages intitulé Ce que le numérique fait au livre, Bertrand Legendre, spécialiste de l’édition, pose sa pierre à l’édifice de la réflexion sur l’impact des technologies du numér..