Related papers: Ewens measures on compact groups and hypergeometri…

We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…

We provide an elementary proof for a theorem due to Petz and R\'effy which states that for a random $n\times n$ unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) $k\times k$…

We apply symmetric function theory to study random processes formed by singular values of products of truncations of Haar distributed symplectic and orthogonal matrices. These product matrix processes are degenerations of Macdonald…

We construct a family of probability measures on the group of Hamiltonian diffeomorphisms of a closed symplectic manifold $(M,\omega)$. We show that these measures are Borel measures with respect to the topology induced by the Hofer metric.…

Data represented by probability measures arise as empirical distributions, posterior distributions, and feature-based representations of complex objects. We study heterogeneity in a population of probability measures through the expected…

We develop the twisting construction for locally compact quantum groups. A new feature, in contrast to the previous work of M. Enock and the second author, is a non-trivial deformation of the Haar measure. Then we construct Rieffel's…

This paper considers random matrices distributed according to Haar measure in different classical compact groups. Utilizing the determinantal point structures of their nontrivial eigenangles, with respect to the $L_1$-Wasserstein distance,…

We prove that when suitably normalized, small enough powers of the absolute value of the characteristic polynomial of random Hermitian matrices, drawn from one-cut regular unitary invariant ensembles, converge in law to Gaussian…

The variance of a linear statistic defined on the symmetric group endowed with the Ewens probability is examined. Despite the dependence of the summands, it can be bounded from above by a constant multiple of the sum of variances. We find…

Given a word $w(x_{1},\ldots,x_{r})$, i.e., an element in the free group on $r$ elements, and an integer $d\geq1$, we study the characteristic polynomial of the random matrix $w(X_{1},\ldots,X_{r})$, where $X_{i}$ are Haar-random…

We obtain large $n$ asymptotics of $n \times n$ Hankel determinants whose weight has a one-cut regular potential and Fisher-Hartwig singularities. We restrict our attention to the case where the associated equilibrium measure possesses…

It is well known that real measures on the circle are characterized by their Herglotz transform, an analytic function in the unit disc. Invariance of the measure under N-multiplication translates into a functional equation for the Herglotz…

Every word $w$ in a free group naturally induces a probability measure on every compact group $G$. For example, if $w=\left[x,y\right]$ is the commutator word, a random element sampled by the $w$-measure is given by the commutator…

For a given orthonormal basis $(f_n)$ on a probability measure space, we want to describe all Markov operators which have the $f_n$ as eigenvectors. We introduce for that what we call the hypergroup property. We study this property in three…

We establish formulae for the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices in terms of certain lattice point count problems. This allows us to establish asymptotic formulae when the…

According to Haar's Theorem, every compact group $G$ admits a unique (regular, right and) left-invariant Borel probability measure $\mu_G$. Let the Haar integral (of $G$) denote the functional $\int_G:\mathcal{C}(G)\ni f\mapsto \int…

The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…

Ensembles of complex symmetric, and complex self dual random matrices are known to exhibit local statistical properties distinct from those of the non-Hermitian Ginibre ensembles. On the other hand, in distinction to the latter, the joint…

Consider a group word w in n letters. For a compact group G, w induces a map G^n \rightarrow G$ and thus a pushforward measure {\mu}_w on G from the Haar measure on G^n. We associate to each word w a 2-dimensional cell complex X(w) and…

For the classical compact Lie groups K = U(N) the autocorrelation functions of ratios of random characteristic polynomials are studied. Basic to our treatment is a property shared by the spinor representation of the spin group with the…