Related papers: Generic Cuspidal Points and Their Localization
The Laplacian eigenvalues of a network play an important role in the analysis of many structural and dynamical network problems. In this paper, we study the relationship between the eigenvalue spectrum of the normalized Laplacian matrix and…
Consider the ensemble of Real Symmetric Toeplitz Matrices, each entry iidrv from a fixed probability distribution p of mean 0, variance 1, and finite higher moments. The limiting spectral measure (the density of normalized eigenvalues)…
We consider the normal matrix ensemble under a general confining potential. We find that the eigenvalues condensate on a compact set in the plane, which we call the spectral droplet. We also study the evolution of incrementally adding a…
We calculate the $k$-point generating function of the correlated Jacobi ensemble using supersymmetric methods. We use the result for complex matrices for $k=1$ to derive a closed-form expression for eigenvalue density. For real matrices we…
(shortened) We determine the transformation matrix T that maps multiple images with resolved features onto one another and that is based on a Taylor-expanded lensing potential close to a point on the critical curve within our…
The simplest patterns of qualitative changes on the configurations of lines of principal curvature} around umbilic points on surfaces whose immersions into $\mathbb R^3$ depend smoothly on a real parameter (codimension one umbilic…
In this work we consider generic losses of rank for complex valued matrix functions depending on two parameters. We give theoretical results that characterize parameter regions where these losses of rank occur. Our main results consist in…
We study the annealed complexity of a random Gaussian homogeneous polynomial on the $N$-dimensional unit sphere in the presence of deterministic polynomials that depend on fixed unit vectors and external parameters. In particular, we…
We discuss the solution of eigenvalue problems associated with partial differential equations that can be written in the generalized form $\m{A}x=\lambda\m{B}x$, where the matrices $\m{A}$ and/or $\m{B}$ may depend on a scalar parameter.…
The local eigenvalue statistics of large random matrices near a hard edge transitioning into a soft edge are described by the Bessel process associated with a large parameter $\alpha$. For this point process, we obtain 1) exponential moment…
We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…
In this paper I will describe some results that have been recently obtained in the study of random Euclidean matrices, i.e. matrices that are functions of random points in Euclidean space. In the case of {\sl translation invariant} matrices…
Recent advances in local models for point processes have highlighted the need for flexible methodologies to account for the spatial heterogeneity of external covariates influencing process intensity. In this work, we introduce tessellated…
For a cuspidal automorphic representation of GL2/Q associated to a modular form, the local and global Langlands correspondences are compatible at all finite places of Q. On the p-adic Coleman-Mazur eigencurve this principle can fail (away…
We study surfaces of constant positive Gauss curvature in Euclidean 3-space via the harmonicity of the Gauss map. Using the loop group representation, we solve the regular and the singular geometric Cauchy problems for these surfaces, and…
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…
We generalize $\epsilon$-pseudospectra and the associated computational algorithms to the generalized eigenvalue problem. Rank one perturbations are used to determine the $\epsilon$-pseudospectra.
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally…