Urban Authorities and Economic Sectors

Taxation on businesses, which makes up two thirds of local authorities' revenues, urges them to widen the range of their economic interventions. The communauté d'agglomération Plaine Commune is one of the most dynamic in the Parisian metropolis and has had considerable expertise at their disposal for 10 years. In order to ensure their economic influence, they now endeavour to stimulate and even structure some economic industries. Unfortunately, a local tax reform in progress may well jeopardise the pattern of development which is presented in this article

Semi-classical analysis of a random walk on a manifold

We prove a sharp rate of convergence to stationarity for a natural random walk on a compact Riemannian manifold $(M,g)$. The proof includes a detailed study of the spectral theory of the associated operator.Comment: Published in at http://dx.doi.org/10.1214/09-AOP483 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Dispersion for the wave equation outside a ball and counterexamples

The purpose of this note is to prove dispersive estimates for the wave equation outside a ball in R^d. If d = 3, we show that the linear flow satisfies the dispersive estimates as in R^3. In higher dimensions d $\ge$ 4 we show that losses in dispersion do appear and this happens at the Poisson spot

Gibbs/Metropolis algorithms on a convex polytope

This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a fixed, finite set of directions, needs some new tools. We get useful bounds on the spectrum and eigenfunctions using Nash and Weyl-type inequalities. The top eigenvalues of the Markov chain are closely related to the Neuman eigenvalues of the polytope for a novel Laplacian.Comment: 21 pages, 1 figur