Search results for "C23"
showing 10 items of 39 documents
Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm
2011
We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincar\'e inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class of convex functionals that a local Poincar\'e inequality is implied by the weak displacement convexity of the functional.
Universal infinitesimal Hilbertianity of sub-Riemannian manifolds
2019
We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations into the space of square-integrable sections of the horizontal bundle, which we obtain on all weighted sub-Finsler manifolds. As an intermediate tool, of independent interest, we show that any sub-Finsler distance can be monotonically approximated from below by Finsler ones. All the results are obtained in the general setting of possibly rank-varying structures.
A short proof of the infinitesimal Hilbertianity of the weighted Euclidean space
2020
We provide a quick proof of the following known result: the Sobolev space associated with the Euclidean space, endowed with the Euclidean distance and an arbitrary Radon measure, is Hilbert. Our new approach relies upon the properties of the Alberti-Marchese decomposability bundle. As a consequence of our arguments, we also prove that if the Sobolev norm is closable on compactly-supported smooth functions, then the reference measure is absolutely continuous with respect to the Lebesgue measure.
Failure of topological rigidity results for the measure contraction property
2014
We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset isometric to $\mathbb{R}$, but does not topologically split. The second space satisfies MCP(2,3) and has diameter $\pi$, which is the maximal possible diameter for a space satisfying MCP(N-1,N), but is not a topological spherical suspension. The latter example gives an answer to a question by Ohta.
Les effets macroéconomiques sur la productivité et les prix de vastes réformes structurelles sur les marchés des biens et du travail
2015
La présente analyse vise à caractériser les effets « directs » et « indirects » des régulations sur le marché des biens ainsi que les effets des régulations sur le marché du travail, sur la productivité et sur les prix. L’analyse est empirique et réalisée via des estimations sur un panel de quatorze pays sur la période 1987-2007, et quand cela est possible sur des donnés sectorielles (treize secteurs manufacturiers et cinq secteurs des services et réseaux). Au terme de ces estimations, il est possible de caractériser les effets de la mise en oeuvre de réformes structurelles. Les réformes structurelles consistent ici en une baisse des indicateurs de régulations sur les marchés des biens et d…
Optimal transport maps on Alexandrov spaces revisited
2018
We give an alternative proof for the fact that in $n$-dimensional Alexandrov spaces with curvature bounded below there exists a unique optimal transport plan from any purely $(n-1)$-unrectifiable starting measure, and that this plan is induced by an optimal map.
Infinitesimal Hilbertianity of Weighted Riemannian Manifolds
2018
AbstractThe main result of this paper is the following: anyweightedRiemannian manifold$(M,g,\unicode[STIX]{x1D707})$,i.e., a Riemannian manifold$(M,g)$endowed with a generic non-negative Radon measure$\unicode[STIX]{x1D707}$, isinfinitesimally Hilbertian, which means that its associated Sobolev space$W^{1,2}(M,g,\unicode[STIX]{x1D707})$is a Hilbert space.We actually prove a stronger result: the abstract tangent module (à la Gigli) associated with any weighted reversible Finsler manifold$(M,F,\unicode[STIX]{x1D707})$can be isometrically embedded into the space of all measurable sections of the tangent bundle of$M$that are$2$-integrable with respect to$\unicode[STIX]{x1D707}$.By following the…
Expectations as Reference Points: Field Evidence from Professional Soccer
2015
We show that professional soccer players and their coaches exhibit reference-dependent behavior during matches. Controlling for the state of the match and for unobserved heterogeneity, we show on a minute-by-minute basis that players breach the rules of the game, measured by the referee’s assignment of cards, significantly more often if their teams are behind the expected match outcome, measured by preplay betting odds of large professional bookmakers. We further show that coaches implement significantly more offensive substitutions if their teams are behind expectations. Both types of behaviors impair the expected ultimate match outcome of the team, which shows that our findings do not si…
Assouad dimension, Nagata dimension, and uniformly close metric tangents
2013
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the to…
High Wage Workers Match with High Wage Firms: Clear Evidence of the Effects of Limited Mobility Bias
2012
Positive assortative matching implies that high productivity workers and firms match together. However, there is almost no evidence of a positive correlation between the worker and firm contributions in two-way fixed-effects wage equations. This could be the result of a bias caused by standard estimation error. Using German social security records we show that the effect of this bias is substantial in samples with limited inter-firm movement. The correlation between worker and firm contributions to wage equations is unambiguously positive.