Related papers: Spectral gap and origami expanders
A lower bound estimate \lambda_2 - \lambda_1 \ge c \lambda_1^{-d / \alpha} (\diam D)^{-d - \alpha} for the spectral gap of the Dirichlet fractional Laplacian on arbitrary bounded domain D is proved. This follows from a variational formula…
Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which…
Graphene's exceptional mechanical properties, including its highest-known stiffness (1 TPa) and strength (100 GPa) have been exploited for various structural applications. However, graphene is also known to be quite brittle, with…
We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals $(2 \sqrt{2},3)$ and $[-3,-2)$ achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on…
We study two different types of gluing for graphs: interface (obtained by choosing a common subgraph as the gluing component) and bridge gluing (obtained by adding a set of edges to the given subgraphs). We introduce formulae for computing…
For general one-matrix models in the large $N$ limit, we introduce the cap amplitude $\psi(b)$ as the expansion coefficient of the 1-form $ydx$ on the spectral curve. We find that the dilaton equation for the discrete volume $N_{g,n}$ of…
In this paper, we obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral…
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…
We study Laplace-type operators on hybrid manifolds, i.e. on configurations consisting of closed two-dimensional manifolds and one-dimensional segments. Such an operator can be constructed by using the Laplace-Beltrami operators on each…
G. Cocco, E. Cadelano, and L. Colombo [Phys. Rev. B 81, 241412(R) (2010)] have suggested that combinations of shear and uniaxial strain can be used to open a band gap in graphene at much lower levels of strain than with the application of…
For $\alpha\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(\xi,|\xi|^\alpha)$. For the corresponding $\alpha$-Strichartz inequalities, by applying the missing mass method and bilinear restriction…
We use Lagrangian specialization to compute the degree of the Gauss map on Theta divisors with transversal $\mathrm{A}_1$ singularities. This computes the Gauss degree for a general abelian variety in the loci $\mathcal{A}^\delta_{t,g-t}$…
In a recent paper Gunnells, Scott and Walden have determined the complete spectrum of the Schreier graph on the symmetric group corresponding to the Young subgroup $S_{n-2}\times S_2$ and generated by initial reversals. In particular they…
It is well known that waves incident upon a crystal are transported only over a limited distance - the Bragg length - before being reflected by Bragg interference. Here, we demonstrate how to send waves much deeper into crystals, by…
In this paper we study quasi-homogeneous affine algebraic varieties, that is, varieties obtained as closures of orbits of suitable group representations. We also discuss one interesting case that has links with the Orthogonal Grassmannian…
We prove that for every surface $\Sigma$ of Euler genus $g$, every edge-maximal embedding of a graph in $\Sigma$ is at most $O(g)$ edges short of a triangulation of $\Sigma$. This provides the first answer to an open problem of Kainen…
Interferometry can completely redirect light, providing the potential for strong and controllable optical forces. However, small particles do not naturally act like interferometric beamsplitters, and the optical scattering from them is not…
The far-field resolution of optical imaging systems is restricted by the Abbe diffraction limit, a direct result of the wave nature of light. One successful technological approach to circumventing this limit is to reduce the effective size…
We establish a general spectral gap theorem for actions of products of groups which may replace Kazhdan's property (T) in various situations. As a main application, we prove that a confined subgroup of an irreducible lattice in a higher…
The calculus of variations for lagrangians which are not functions on the tangent bundle, but sections certain affine bundles is developed. We follow a general approach to variational principles which admits boundary terms of variations.