Related papers: Approximate factorization and concentration for ch…

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…

Many finite groups, including all finite non-abelian simple groups, can be symmetrically generated by involutions. In this paper we give an algorithm to symmetrically represent elements of finite groups and to transform symmetrically…

In this paper we study the Frobenius characters of the invariant subspaces of the tensor powers of a representation V. The main result is a formula for these characters for a polynomial functor of V involving the characters for V. The main…

We consider the proportion of zero entries in the character table of a sequence of reductive groups over a finite field. We prove an asymptotic lower bound when the reductive group is fixed and the size of the finite field increases.…

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner…

This is a brief report on some recent large-scale Monte Carlo simulations for approximating the density of zeros in character tables of large symmetric groups. Previous computations suggested that a large fraction of zeros cannot be…

For a given symmetric tensor, we aim at finding a new one whose symmetric rank is small and that is close to the given one. There exist linear relations among the entries of low rank symmetric tensors. Such linear relations can be expressed…

In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic…

We study random typical minimal factorizations of the $n$-cycle, which are factorizations of $(1, \ldots,n)$ as a product of $n-1$ transpositions, chosen uniformly at random. Our main result is, roughly speaking, a local convergence theorem…

In this paper, we count factorizations of Coxeter elements in well-generated complex reflection groups into products of reflections. We obtain a simple product formula for the exponential generating function of such factorizations, which is…

We investigate the relationship between symmetric functions and the representation theory of operads, relative operads, and props. We extend the classical character map for symmetric sequences to relative bisymmetric sequences and symmetric…

By invoking supersymmetry, we found a condition under which the Stark effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable. The exact solvability condition for the interaction…

Probabilistic algorithms are applied to prove theorems about the finite general linear and unitary groups which are typically proved by techniques such as character theory and Moebius inversion. Among the theorems studied are Steinberg's…

While Random Matrix Theory has successfully modeled many quantities of families of L-functions, it frequently cannot see the family's arithmetic. In some situations this requires an extended theory that inserts arithmetic factors depending…

This text investigates relations between two well-known family of algorithms, matrix factorisations and recursive linear filters, by describing a probabilistic model in which approximate inference corresponds to a matrix factorisation…

Correlation matrices are the sub-class of positive definite real matrices with all entries on the diagonal equal to unity. Earlier work has exhibited a parametrisation of the corresponding Cholesky factorisation in terms of partial…

Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…

Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…

We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…

Voiculescu's notion of asymptotic free independence applies to a wide range of random matrices, including those that are independent and unitarily invariant. In this work, we generalize this notion by considering random matrices with a…