相关论文: Row products of random matrices
Consider the following parameterized counting variation of the classic subset sum problem, which arises notably in the context of higher homotopy groups of topological spaces: Let $\mathbf{v} \in \mathbb{Q}^d$ be a rational vector, $(T_{1},…
We study the spectral norm of matrices M that can be factored as M=BA, where A is a random matrix with independent mean zero entries, and B is a fixed matrix. Under the (4+epsilon)-th moment assumption on the entries of A, we show that the…
A Riordan array is defined by its production matrix. In this paper, we explore the notion of the second production matrix of a Riordan array, characterizing the matrix that is generated by it. We indicate how this procedure can be…
We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…
We study the problem of answering \emph{$k$-way marginal} queries on a database $D \in (\{0,1\}^d)^n$, while preserving differential privacy. The answer to a $k$-way marginal query is the fraction of the database's records $x \in \{0,1\}^d$…
We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Matrix factorization is a simple and effective solution to the recommendation problem. It has been extensively employed in the industry and has attracted much attention from the academia. However, it is unclear what the low-dimensional…
Consider a stochastic matrix $P$ and diagonal matrix $D.$ In this work, we introduce Tilted matrices. A Tilted matrix is the product $D'PD$, where $D'$ is a diagonal normalization that makes the product stochastic. We then provide several…
It is known that a category of many-sorted algebras on pure sets of similarity type is "concretely equivalent" to a category of single-sorted algebras. In this paper, we characterize a single-sorted variety that corresponds to a many-sorted…
To every product of $2\times2$ matrices, there corresponds a one-dimensional Schr\"{o}dinger equation whose potential consists of generalised point scatterers. Products of {\em random} matrices are obtained by making these interactions and…
We introduce a family of models, which we name matrix models associated with children's drawings -- the so-called dessin d'enfant. Dessins d'enfant are graphs of a special kind drawn on a closed connected orientable surface (in the sky).…
The matrix-variate normal distribution is a popular model for high-dimensional transposable data because it decomposes the dependence structure of the random matrix into the Kronecker product of two covariance matrices: one for each of the…
We formulate conjectures regarding the maximum value and maximizing matrices of the permanent and of diagonal products on the set of stochastic matrices with bounded rank. We formulate equivalent conjectures on upper bounds for these…
The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization recently proposed is the k-anonymity. This approach requires that the rows in a table are clustered in sets…
It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation…
We propose a relaxed privacy definition called {\em random differential privacy} (RDP). Differential privacy requires that adding any new observation to a database will have small effect on the output of the data-release procedure. Random…
We study containment and uniqueness problems concerning matrix convex sets. First, to what extent is a matrix convex set determined by its first level? Our results in this direction quantify the disparity between two product operations,…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
In this paper we consider four basic multidimensional matrix operations (outer product, Kronecker product, contraction, and projection) and two derivative operations (dot and circle products). We start with the interrelations between these…