相关论文: A general decoupling inequality for finite Gaussia…
In the matrix sensing problem, one wishes to reconstruct a matrix from (possibly noisy) observations of its linear projections along given directions. We consider this model in the high-dimensional limit: while previous works on this model…
We utilise the two principles of decoupling introduced in arXiv:2407.16108 to prove the following conditional result: assuming uniform decoupling for graphs of polynomials in all dimensions with identically zero Gaussian curvature, we can…
Gaussian filters have applications in a variety of areas in computer science, from computer vision to speech recognition. The collapsing sum is a matrix operator that was recently introduced to study Gaussian filters combinatorially. In…
In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…
We prove generalized Gaffney inequalities and the discrete compactness for finite element differential forms on $s$-regular domains, including general Lipschitz domains. In computational electromagnetism, special cases of these results have…
In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…
A combinatorial proof of the Gaussian product inequality (GPI) is given under the assumption that each component of a centered Gaussian random vector $\boldsymbol{X} = (X_1, \ldots, X_d)$ of arbitrary length can be written as a linear…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
A problem that is frequently encountered in a variety of mathematical contexts, is to find the common invariant subspaces of a single, or set of matrices. A new method is proposed that gives a definitive answer to this problem. The key idea…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We prove optimal local law, bulk universality and non-trivial decay for the off-diagonal elements of the resolvent for a class of translation invariant Gaussian random matrix ensembles with correlated entries.
We study decompositions of the global NVALUE constraint. Our main contribution is theoretical: we show that there are propagators for global constraints like NVALUE which decomposition can simulate with the same time complexity but with a…
This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the…
In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…
Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…
We calculate the average differential entropy of a $q$-component Gaussian mixture in $\mathbb R^n$. For simplicity, all components have covariance matrix $\sigma^2 {\mathbf 1}$, while the means $\{\mathbf{W}_i\}_{i=1}^{q}$ are i.i.d.…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued…
The matrix version of the entropy-power inequality for real or complex coefficients and variables is proved using a transportation argument that easily settles the equality case. An application to blind source extraction is given.
We review and generalize the recently introduced framework of entropy vectors for detecting and quantifying genuine multipartite entanglement in high dimensional multicomponent quantum systems. We show that these ideas can be extended to…