Related papers: Principal Eigenvalue and Landscape Function of the…

We generalize Minami's estimate for the Anderson model and its extensions to $n$ eigenvalues, allowing for $n$ arbitrary intervals and arbitrary single-site probability measures with no atoms. As an application, we derive new results about…

We establish rigorous quantitative inequalities for the first eigenvalue of the generalized $p$-Robin problem, for both the classical diffusion absorption case, where the Robin boundary parameter $\alpha$ is positive, and the…

This paper is concerned with generalizations of the notion of principal eigenvalue in the context of space-time periodic cooperative systems. When the spatial domain is the whole space, the Krein-Rutman theorem cannot be applied and this…

We study the existence of principal eigenvalues and principal eigenfunctions for weighted eigenvalue problems of the form: \begin{equation*} - \mbox{div} ( L (x) |\nabla u|^{p-2} \nabla u ) = \lambda K(x) |u|^{p-2} u \hspace{.1cm} \mbox {…

In a random unitary matrix model at large N, we study the properties of the expectation value of the character of the unitary matrix in the rank k symmetric tensor representation. We address the problem of whether the standard semiclassical…

Spectral methods include a family of algorithms related to the eigenvectors of certain data-generated matrices. In this work, we are interested in studying the geometric landscape of the eigendecomposition problem in various spectral…

Findings by M. L. Lyra, S. Mayboroda and M. Filoche relate invertibility and positivity of a class of discrete Schr\"odinger matrices with the existence of the "Landscape Function", which provides an upper bound on all eigenvectors…

The circular and Jacobi ensembles of random matrices have their eigenvalue support on the unit circle of the complex plane and the interval $(0,1)$ of the real line respectively. The averaged value of the modulus of the corresponding…

It is well known that, in the study of the dynamical properties of nonlinear evolution system with nonlocal dispersals, the principal eigenvalue of linearized system play an important role. However, due to lack of compactness, in order to…

We study the generalized eigenvalue problem on the whole space for a class of integro-differential elliptic operators. The nonlocal operator is over a finite measure, but this has no particular structure. Some of our results even hold for…

We show that the spacing between eigenvalues of the discrete 1D Hamiltonian with arbitrary potentials which are bounded, and with Dirichlet or Neumann Boundary Conditions is bounded away from zero. We prove an explicit lower bound, given by…

We study the behavior of eigenvalues of matrix P_N + Q_N where P_N and Q_N are two N -by-N random orthogonal projections. We relate the joint eigenvalue distribution of this matrix to the Jacobi matrix ensemble and establish the universal…

We describe the eigenvalues and the eigenspaces of the adjacency matrices of subgraphs of the Hamming cube induced by Hamming balls, and more generally, by a union of adjacent concentric Hamming spheres. As a corollary, we extend the range…

We prove that in dimension one the non-real eigenvalues of the non-Hermitian Anderson (NHA) model with a selfaveraging potential are regularly spaced. The class of selfaveraging potentials which we introduce in this paper is very wide and…

We describe a general framework to depict the space of Lorentz invariant effective field theories, which we call the landscape, given any kind of gauge symmetry and field content. Various operator bases in the landscape can be…

We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The projection subspaces are constructed iteratively by means of…

We investigate the validity of the assertion that eternal inflation populates the landscape of string theory. We verify that bubble solutions do not satisfy the Klein Gordon equation for the landscape potential. Solutions to the landscape…

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic…

We prove the existence of a principal eigenvalue associated to the $\infty$-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the…

A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…