Extreme gaps between eigenvalues of random matrices

This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth smallest gap, normalized by a factor $n^{-4/3}$, has a limiting density proportional to $x^{3k-1}e^{-x^3}$. Concerning the largest gaps, normalized by $n/\sqrt{\log n}$, they converge in ${\mathrm{L}}^p$ to a constant for all $p>0$. These results are compared with the extreme gaps between zeros of the Riemann zeta function.Comment: Published in at http://dx.doi.org/10.1214/11-AOP710 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Smoothed Affine Wigner Transform

We study a generalization of Husimi function in the context of wavelets. This leads to a nonnegative density on phase-space for which we compute the evolution equation corresponding to a Schr\"Aodinger equation

Vulcanism and Prehistory in the massif central of France : Future Prospects for Sustainable Development of Rural Highlands

If recent huge projects in Auvergne, as Vulcania near Clermont-Ferrand for example, try to use vulcanism as a matter of sustainable local development, attracting either seasonal touristic flow or all-year academic activities, the remote highlands of Velay begin to discover that archaeology and vulcanism make an original combination to increase interest of populations and can be a key for sustainable rural development.volcanisme;archéologie;développement local;développement durable;Massif central;Haute-Loire

Relationships between hydraulic traits and habitat preference for six Acer species occurring in the French Alps

Xylem hydraulic properties and vulnerability to cavitation were studied in six Acer species which occur, in the French Alps, along a soil moisture gradient from the moist valleys to the drier mountain stands. The results obtained suggest that a relationship existed between hydraulic properties and the species moisture preference. Maples located in dry zones (A. opalus, A. monspessulanum) proved more resistant to drought-induced cavitation than species that occurred in an irrigated area (A. negundo, A. pseudoplatanus, A. platanoides, A. campestre). The most vulnerable species to cavitation (A. negundo, A. pseudoplatanus, A. platanoides, A. campestre) showed the highest hydraulic conductances, whereas more cavitation-resistant species (A. opalus, A. monspessulanum) had the lowest conductances. This suggests a tradeoff between hydraulic efficiency and cavitation vulnerability. The possible ecological significances of these data are discussed in relation to the distribution of Acer species in their natural habitats

Un cadre téphrostratigraphique réactualisé pour la préhistoire tardiglaciaire et holocène de Limagne (Massif central, France)

pdf du manuscrit avant révisionNational audienceFrom the Older Dryas to the Atlantic Period, ten pyroclastic formations originating from trachyandesitic and trachytic eruptions covered the plain of the Limagne d'Auvergne and have been preserved in various depositional contexts. They are useful isochronic markers for archaeologists examining their impact on prehistoric behaviours and settlements.Dix recouvrements de tephras, suffisamment importants pour avoir ete préservés en stratigraphie dans des environnements sédimentaires divers, ont affecté la Limagne du Dryas ancien à l'Atlantique. Ils caractérisent des éruptions pour l'essentiel à magmas trachyandésitiques et trachytiques. Outre leur rôle incontestable de marqueurs isochroniques, ils incitent à reconsidérer l'impact du volcanisme de la Chaîne des Puys sur l'environnement des peuplements préhistoriques contemporains

Enantioselective Insertion of Carbenoids into N-H Bonds Catalyzed by Chiral Bicyclo Bisoxazoline Copper(I) Complexes

International audienceChiral copper(I)-bicyclobisoxazoline complexes were found to catalyse the insertion of α-diazocarbonyl compounds into N-H bonds of aniline derivatives. The insertion reactions proceeded with high yields (78-99%) and enantioselectivities of up to 81% for the different α-diazopropionates. A predominant effect of the nature and the position of the substituents on the enantiocontrol of the reaction was observe

Les retombées volcaniques distales de la Chaîne des Puys

pdf du manuscrit. Contacter l'auteur pour une version illustrée.Reconnaissance des éruptions de la Chaîne des Puys par l'étude des retombées distales de cendres volcaniques enregistrées dans les dépôts de la plaine de Limagne

Hommes et volcans en Basse Auvergne préhistorique

pdf du manuscritNational audienceFrom 160 to 30 ka BP, Western Limagne is strongly affected by local explosive vulcanism, lava flows and distal tephra falls from the old Chaîne des Puys. Fromm the Older Dryas to the Atlantic Period, ten pyroclastic formations originating from trachyandesitic and trachytic eruptions covered the plain of the Limagne d'Auvergne and have been preserved in various depositional contexts. They are useful isochronic markers for archaeologists examining their impact on prehistoric behaviours and settlements.De 160 à 30 ka BP, la Limagne occidentale est le siège d'un volcanisme parfois violemment explosif et soumise aux effets secondaires des éruptions de la phase ancienne de la Chaîne des Puys. De 12 à 6 ka BP, dix recouvrements de téphras, suffisamment importants pour avoir été préservés en stratigraphie dans des environnements sédimentaires divers, ont affecté la Limagne. Ils caractérisent des éruptions pour l'essentiel à magmas trachyandésitiques et trachytiques et sont de bons marqueurs isochroniques. L'homme préhistorique a subi ce volcanisme qui a profondément transformé son cadre de vie