Related papers: Probabilistic estimates for tensor products of ran…

Johnson-Lindenstrauss lemma states random projections can be used as a topology preserving embedding technique for fixed vectors. In this paper, we try to understand how random projections affect probabilistic properties of random vectors.…

We prove genuinely multilinear weighted estimates for singular integrals in product spaces. The estimates complete the qualitative weighted theory in this setting. Such estimates were previously known only in the one-parameter situation.…

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…

We show that every admissible irreducible representation of a product of two locally compact groups is a tensor product of admissible irreducible representations of the factors.

We prove a connectedness result for products of weighted projective spaces.

We prove uniform estimates for the expected value of averages of order statistics of matrices in terms of their largest entries. As an application, we obtain similar probabilistic estimates for $\ell_p$ norms via real interpolation.

In this paper matrix quantitative weighted estimates on spaces of homogeneous type, such as endpoint estimates, strong type estimates are provided. To that end we extend some earlier results on convex body domination due to Nazarov,…

This paper focuses on the $GL_n$ tensor product algebra, which encapsulates the decomposition of tensor products of arbitrary finite dimensional irreducible representations of $GL_n$. We will describe an explicit basis for this algebra.…

We investigate tensor products of random matrices, and show that independence of entries leads asymptotically to $\varepsilon$-free independence, a mixture of classical and free independence studied by M{\l}otkowski and by Speicher and…

We prove that for almost square tensor product grids and certain sets of bivariate polynomials the Vandermonde determinant can be factored into a product of univariate Vandermonde determinants. This result generalizes the conjecture [Lemma…

The main result of this paper is a bi-parameter T(b) theorem for the case that b is a tensor product of two pseudo-accretive functions. In the proof, we also discuss the L^2 boundedness of different types of the b-adapted bi-parameter…

We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from the same set of local matrices (or tensors) that are determined from an infinite lattice system in…

We introduce a simple algorithm that efficiently computes tensor products of Pauli matrices. This is done by tailoring the calculations to this specific case, which allows to avoid unnecessary calculations. The strength of this strategy is…

The simple product formulae for derivatives of scalar functions raised to different powers are generalized for functions which take values in the set of symmetric positive definite matrices. These formulae are fundamental in derivation of…

Given $d \in \mathbb{N}$, we establish sum-product estimates for finite, non-empty subsets of $\mathbb{R}^d$. This is equivalent to a sum-product result for sets of diagonal matrices. In particular, let $A$ be a finite, non-empty set of $d…

In this note we consider the point process of eigenvalues of the tensor product of two independent random unitary matrices of size m by m and n by n. When n becomes large, the process behaves like the superposition of m independent sine…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and…

We describe one interpretation of the q-Catalan numbers in frameworks of random matrix theory and weighted partitions of the set of integers.

This paper presents iterative methods for solving tensor equations involving the T-product. The proposed approaches apply tensor computations without matrix construction. For each initial tensor, these algorithms solve related problems in a…