Volume distribution of nodal domains of random band-limited functions

Eigenvectors of Random Graphs: Nodal Domains

We initiate a systematic study of eigenvectors of random graphs. Whereas much is known about eigenvalues of graphs and how they reflect properties of the underlying graph, relatively little is known about the corresponding eigenvectors. Our main focus in this paper is on the nodal domains associated with the different eigenfunctions. In the analogous realm of Laplacians of Riemannian manifolds,...

Band-limited Functions: / / -convergence

the pathology of historical texts translation: a study of persian translations of 7th volume of cambridge history of iran

ترجمه با گسترش زبان آغاز شده و اهمیت آن روز به روز افزایش می یابد، و برای اولین بار به عنوان شاخه ای از دانش و روشی برای انتقال علوم، فرهنگ و تجربه در در دوره قاجار در ایران آغاز شد. در حقیقت متون تاریخی از اولین متونی هستند که در ایران ترجمه شدند چرا که به سیاستمداران آن دوره کمک می کردند تا به علل موفقیت جهان غرب و پیشرفت هایشان در طول تاریخ پی ببرند، بنابراین به تدریج ترجمه این گونه متون رون...

Relevant Sampling of Band-limited Functions

We study the random sampling of band-limited functions of several variables. If a band-limited function with bandwidth has its essential support on a cube of volume R, then O(Rd logR) random samples suffice to approximate the function up to a given error with high probability.

A Local Volume Estimate for Nodal Domains of Laplace Eigenfunctions

Let M either be a closed real analytic Riemannian manifold or a closed C∞-Riemannian surface. We estimate from below the volume of a nodal domain component in an arbitrary ball, provided that this component enters the ball deeply enough. The proof combines a generalized form of Hadamard’s Three Circles Theorem due to Nadirashvili, Rapid Growth of Eigenfunctions in Narrow Domains and the Donnell...