Gaussian Constants

Improved Bounds on Restricted Isometry Constants for Gaussian Matrices

The Restricted Isometry Constants (RIC) of a matrix A measures how close to an isometry is the action of A on vectors with few nonzero entries, measured in the `2 norm. Specifically, the upper and lower RIC of a matrix A of size n ×N is the maximum and the minimum deviation from unity (one) of the largest and smallest, respectively, square of singular values of all `N k ́ matrices formed by taki...

NMR Spin-Spin Coupling Constants in Gaussian 03 for dummies

Restricted Isometry Constants for Gaussian and Rademacher matrices

Restricted Isometry Constants (RICs) are a pivotal notion in Compressed Sensing as these constants finely assess how a linear operator is conditioned on the set of sparse vectors and hence how it performs in stable and robust sparse regression (SRSR). While it is an open problem to construct deterministic matrices with apposite RICs, one can prove that such matrices exist using random matrices ...

Duality relations for elastic constants of the classical Gaussian core model.

The many-body Gaussian core model involves a potential energy function that consists of a sum of repelling pair interactions, each of which is a simple Gaussian function of distance. This paper examines the linear elastic response of the model for its stable lattices at absolute zero temperature, in D=1, 2, and 3 dimensions. Owing to the fact that the Gaussian function is self-similar under Fou...

Bounds of restricted isometry constants in extreme asymptotics: formulae for Gaussian matrices

Restricted Isometry Constants (RICs) provide a measure of how far from an isometry a matrix can be when acting on sparse vectors. This, and related quantities, provide a mechanism by which standard eigen-analysis can be applied to topics relying on sparsity. RIC bounds have been presented for a variety of random matrices and matrix dimension and sparsity ranges. We provide explicitly formulae f...