Equidistribution estimates for Fekete points on complex manifolds

We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich-Wasserstein distance of the Fekete points to its limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles.Comment: Improved version with a sharp decay rate in the estimate of the Kantorovich-Wasserstein distance of the Fekete points to its limiting measure (Theorem 2

Carleson Measures and Logvinenko-Sereda sets on compact manifolds

Given a compact Riemannian manifold $M$ of dimension $m\geq 2$, we study the space of functions of $L^2(M)$ generated by eigenfunctions of eigenvalues less than $L\geq 1$ associated to the Laplace-Beltrami operator on $M$. On these spaces we give a characterization of the Carleson measures and the Logvinenko-Sereda sets

Configurations of balls in Euclidean space that Brownian motion cannot avoid

We consider a collection of balls in Euclidean space and the problem of determining if Brownian motion has a positive probability of avoiding all the ball

Experimental Evaluation of Wireless Mesh Networks: A Case Study and Comparison

Price of WiFi devices has decreased dramatically in recent years, while new standards, as 802.11n, have multiplied its performance. This has fostered the deployment of Wireless Mesh networks (WMN), putting into practice concepts evolved from more than a decade of research in Ad Hoc networks. Nevertheless, evolution of WMN it is in its infancy, as shows the growing and diverse number of scenarios where WMN are being deployed. In these paper we analyze a particular case study of a Wireless Community Mesh Network, and we compare it with a selected experimental WMN studies found in the literature

Marcinkiewicz-Zygmund inequalities

We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities