相关论文: A general decoupling inequality for finite Gaussia…

The paper contains two main parts: in the first part, we analyze the general case of $p\geq 2$ matrices coupled in a chain subject to Cauchy interaction. Similarly to the Itzykson-Zuber interaction model, the eigenvalues of the Cauchy chain…

We study algorithms called rank-revealers that reveal a matrix's rank structure. Such algorithms form a fundamental component in matrix compression, singular value estimation, and column subset selection problems. While column-pivoted QR…

We consider the singular vectors of any $m \times n$ submatrix of a rectangular $M \times N$ Gaussian matrix and study their asymptotic overlaps with those of the full matrix, in the macroscopic regime where $N \,/\, M\,$, $m \,/\, M$ as…

We establish the universality of the singular numbers in random matrix products over $\mathrm{GL}_n(\mathbb{Q}_p)$ as the number of products approaches infinity, with a fixed $n\ge 1$. We demonstrate that, under a broad class of…

The non-decreasing condition on g-vectors is introduced. Our study shows that this condition is both necessary and sufficient to ensure that the generically indecomposable direct summands of a given g-vector are linearly independent.…

Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix…

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the…

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…

Algebraic geometry, although little explored in signal processing, provides tools that are very convenient for investigating generic properties in a wide range of applications. Generic properties are properties that hold "almost…

Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…

The paper is to prove the Gaussian correlation conjecture stating that, under the standard Gaussian measure, the measure of the intersection of any two symmetric convex sets is greater than or equal to the product of their measures.…

A random matrix is likely to be well conditioned, and motivated by this well known property we employ random matrix multipliers to advance some fundamental matrix computations. This includes numerical stabilization of Gaussian elimination…

The starting point of this work is a theorem due to Maxwell characterizing the distribution of a Gaussian vector with at least two coordinates. We define the Gaussian orthogonal, unitary and symplectic tensor ensembles for notions of real…

The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see [1]). We present a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a…

Expanding a lower-dimensional problem to a higher-dimensional space and then projecting back is often beneficial. This article rigorously investigates this perspective in the context of finite mixture models, namely how to improve inference…

The paper provides a new integral formula for the largest Lyapunov exponent of Gaussian matrices, which is valid in the real, complex and quaternion-valued cases. This formula is applied to derive asymptotic expressions for the largest…

We obtain the explicit rate of convergence $N^{-1/2 + \epsilon}$ for the gaps of generalized Wigner matrices in the bulk of the spectrum, for distributions of matrix entries possibly atomic and supported on enough points. The proof proceeds…

We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these…

Leveraging a recently proposed notion of relative entropy in general probabilistic theories (GPT), we prove a finite de Finetti representation theorem for general convex bodies. We apply this result to address a fundamental question in…

We introduce a general framework for testing goodness-of-fit for Gaussian graphical models in both the low- and high-dimensional settings. This framework is based on a novel algorithm for generating exchangeable copies by conditioning on…