Related papers: On construction and analysis of sparse random matr…

Kim defined a very general combinatorial abstraction of the diameter of polytopes called subset partition graphs to study how certain combinatorial properties of such graphs may be achieved in lower bound constructions. Using Lov\'asz'…

We study the random loop model with crosses and bars on sparse random graphs. Our main objective is to prove the existence of macroscopic loops, in the sense that a loop visits a positive proportion of the vertices. We develop a…

This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…

Structurally random matrices (SRMs) are a practical alternative to fully random matrices (FRMs) when generating compressive sensing measurements because of their computational efficiency and their universality with respect to the sparsifing…

We study random matrices with independent subgaussian columns. Assuming each column has a fixed Euclidean norm, we establish conditions under which such matrices act as near-isometries when restricted to a given subset of their domain. We…

Statistical network modeling has focused on representing the graph as a discrete structure, namely the adjacency matrix, and considering the exchangeability of this array. In such cases, the Aldous-Hoover representation theorem (Aldous,…

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…

In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted…

Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted and stored using far fewer measurements than done by conventional means employing Nyquist sampling theorem. Since many naturally occurring signals are…

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…

In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying…

Let S and T be vectors of positive integers with the same sum. We study the uniform distribution on the space of simple bipartite graphs with degree sequence S in one part and T in the other; equivalently, binary matrices with row sums S…

We compute the spectral density for ensembles of of sparse symmetric random matrices using replica, managing to circumvent difficulties that have been encountered in earlier approaches along the lines first suggested in a seminal paper by…

The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…

An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…

This paper investigates the behaviour of the spectrum of generally correlated Gaussian random matrices whose columns are zero-mean independent vectors but have different correlations, under the specific regime where the number of their…

We study the typical structure of a sparse Erd\H{o}s--R\'enyi random graph conditioned on the lower tail subgraph count event. We show that in certain regimes, a typical graph sampled from the conditional distribution resembles the entropy…

Two landmark results in combinatorial random matrix theory, due to Koml\'os and Costello-Tao-Vu, show that discrete random matrices and symmetric discrete random matrices are typically nonsingular. In particular, in the language of graph…

We give an algorithm that generates a uniformly random contingency table with specified marginals, i.e. a matrix with non-negative integer values and specified row and column sums. Such algorithms are useful in statistics and combinatorics.…