Subelliptic Li-Yau estimates on three dimensional model spaces

We describe three elementary models in three dimensional subelliptic geometry which correspond to the three models of the Riemannian geometry (spheres, Euclidean spaces and Hyperbolic spaces) which are respectively the SU(2), Heisenberg and SL(2) groups. On those models, we prove parabolic Li-Yau inequalities on positive solutions of the heat equation. We use for that the $\Gamma_{2}$ techniques that we adapt to those elementary model spaces. The important feature developed here is that although the usual notion of Ricci curvature is meaningless (or more precisely leads to bounds of the form $-\infty$ for the Ricci curvature), we describe a parameter $\rho$ which plays the same role as the lower bound on the Ricci curvature, and from which one deduces the same kind of results as one does in Riemannian geometry, like heat kernel upper bounds, Sobolev inequalities and diameter estimates

Log-Harnack Inequality for Stochastic Differential Equations in Hilbert Spaces and its Consequences

A logarithmic type Harnack inequality is established for the semigroup of solutions to a stochastic differential equation in Hilbert spaces with non-additive noise. As applications, the strong Feller property as well as the entropy-cost inequality for the semigroup are derived with respect to the corresponding distance (cost function)

String effects and the distribution of the glue in mesons at finite temperature

The distribution of the gluon action density in mesonic systems is investigated at finite temperature. The simulations are performed in quenched QCD for two temperatures below the deconfinment phase. Unlike the gluonic profiles displayed at T=0, the action density iso-surfaces display a prolate-spheroid like shape. The curved width profile of the flux-tube is found to be consistent with the prediction of the free Bosonic string model at large distances.Comment: 14 pages,10 figure

Un déterminant de l'innovation technique en agriculture : les coordinations sur le travail dans la production bananière

The growth of the international market of the horticultural products is made possible by the globalization of an intensive mode of production in synthetic products which mobilizes salaried workers. In the Antilles changes in technological trajectories enables the consideration of other modes of production. This article brings to light how the technical innovation allowing a decrease in the necessity to use pesticides is dependent on an adaptation of the coordination in the mobilization of the salaried work. For this purpose we compare two systems of the use of manual labour between Martinique and Guadeloupe by widening on certain aspects in the transnational. The comparison is based on the characterization of these systems in which manual labour is used and the indicators of performance of the sectors of banana as well as on the adaptation of the technical changes. ...French Abstract : La croissance du marché international des produits horticoles se réalise par la globalisation d'un mode de production intensif en produits de synthèses qui mobilise une main d'oeuvre salariée. Dans les Antilles des changements de trajectoires technologiques permettent d'envisager d'autres modes de production. Cet article met en évidence comment l'innovation technique permettant de diminuer le recours aux pesticides est tributaire d'une adaptation des coordinations dans la mobilisation du travail salarié. Pour cela nous caractérisons les systèmes d'emploi de la main d'oeuvre salarié entre différentes origines et leurs impact sur des indicateurs de performance des filières de banane et d'adaptation des changements techniques.BANANA; WORK; INNOVATION; PESTICIDE; ANTILLES

Uniform convergence to equilibrium for granular media

We study the long time asymptotics of a nonlinear, nonlocal equation used in the modelling of granular media. We prove a uniform exponential convergence to equilibrium for degenerately convex and non convex interaction or confinement potentials, improving in particular results by J. A. Carrillo, R. J. McCann and C. Villani. The method is based on studying the dissipation of the Wasserstein distance between a solution and the steady state

Dimension dependent hypercontractivity for Gaussian kernels

We derive sharp, local and dimension dependent hypercontractive bounds on the Markov kernel of a large class of diffusion semigroups. Unlike the dimension free ones, they capture refined properties of Markov kernels, such as trace estimates. They imply classical bounds on the Ornstein-Uhlenbeck semigroup and a dimensional and refined (transportation) Talagrand inequality when applied to the Hamilton-Jacobi equation. Hypercontractive bounds on the Ornstein-Uhlenbeck semigroup driven by a non-diffusive L\'evy semigroup are also investigated. Curvature-dimension criteria are the main tool in the analysis.Comment: 24 page

The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds

The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities.Comment: Update: Added section + Correction of typo