相关论文: Restricted Eigenvalue Conditions on Subgaussian Ra…

Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the…

Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state functions in random matrix theory. We develop this approach for…

We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column)…

In [8] the author of this paper continued the research on the complex-valued discrete random variables $X_l(m,N)$ ($0\le l\le N-1$, $1\le M\le N)$ recently introduced and studied in [24]. Here we extend our results by considering $X_l(m,N)$…

The complete eigenstructure, or structural data, of a rational matrix $R(s)$ is comprised by its invariant rational functions, both finite and at infinity, which in turn determine its finite and infinite pole and zero structures,…

We define a graph to be $S$-regular if it contains an equitable partition given by a matrix $S$. These graphs are generalizations of both regular and bipartite, biregular graphs. An $S$-regular matrix is defined then as a matrix on an…

In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the…

Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…

An important consideration for variable selection in interaction models is to design an appropriate penalty that respects hierarchy of the importance of the variables. A common theme is to include an interaction term only after the…

The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…

Pseudospectral analysis serves as a powerful tool in matrix computation and the study of both linear and nonlinear dynamical systems. Among various numerical strategies, random sampling, especially in the form of rank-$1$ perturbations,…

Let $v$ be a submultiplicative weight. Then we prove that $v$ satisfies GRS-condition, if and only if $v\cdot e^{-\ep |\cdo |}$ is bounded for every positive $\ep$. We use this equivalence to establish identification properties between…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

Motivated by the popularity of stochastic rounding in the context of machine learning and the training of large-scale deep neural network models, we consider stochastic nearness rounding of real matrices $\mathbf{A}$ with many more rows…

We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…

In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…

This paper concerns the characterisation of second order marginals for random sets in a discrete setting. Under the instance of unit covariances, this problem possesses a combinatorial symmetry, exploited jointly in the companion paper to…

Variational minimization of the ground-state energy as a function of the two-electron reduced density matrix (2-RDM), constrained by necessary $N$-representability conditions, provides a polynomial-scaling approach to studying strongly…

We observe that the distribution of the eigenvalues of an $N$-by-$N$ GUE random matrix is log-concave on $\mathbb{R}^N$, and that the same is true for the law of a single gap between two consecutive eigenvalues. We use this observation to…

Conditions are presented for different types of identifiability of discrete variable models generated over an undirected graph in which one node represents a binary hidden variable. These models can be seen as extensions of the latent class…