Related papers: Common frequently hypercyclic random vectors
A family of random matrices is said to converge strongly to a limiting family of operators if the operator norm of every noncommutative polynomial of the matrices converges to that of the limiting operators. Recent developments surrounding…
We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improving upon the known size and structure of the set of strong…
Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian inference in statistical modeling. However, the existing VB algorithms are restricted to cases where the likelihood is tractable, which precludes the use of VB in many…
We consider generalized inversions and descents in finite Weyl groups. We establish Coxeter-theoretic properties of indicator random variables of positive roots such as the covariance of two such indicator random variables. We then compute…
We introduce the evolving categories multinomial (ECM) distribution for multivariate count data taken over time. This distribution models the counts of individuals following iid stochastic dynamics among categories, with the number and…
We consider the singular vectors of any $m \times n$ submatrix of a rectangular $M \times N$ Gaussian matrix and study their asymptotic overlaps with those of the full matrix, in the macroscopic regime where $N \,/\, M\,$, $m \,/\, M$ as…
Conditions for positive and polynomial recurrence have been proposed for a class of reliability models of two elements with transitions from working state to failure and back. As a consequence, uniqueness of stationary distribution of the…
Chan and Seceleanu have shown that if a weighted shift operator on $\ell^p(\mathbb{Z})$, $1\leq p<\infty$, admits an orbit with a non-zero limit point then it is hypercyclic. We present a new proof of this result that allows to extend it to…
A complete characterization of the similarity between two operator-valued multishifts with invertible operator weights is obtained purely in terms of operator weights. This generalizes several existing results of the unitary equivalence of…
The (relevance) weighted likelihood was introduced to formally embrace a variety of statistical procedures that trade bias for precision. Unlike its classical counterpart, the weighted likelihood combines all relevant information while…
Data vectors generalise finite multisets: they are finitely supported functions into a commutative monoid. We study the question if a given data vector can be expressed as a finite sum of others, only assuming that 1) the domain is…
A weight-dependent generalization of the binomial theorem for noncommuting variables is presented. This result extends the well-known binomial theorem for q-commuting variables by a generic weight function depending on two integers. For a…
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure…
By prepending zeros to a given sequence Hankel determinants of backward shifts of this sequence become meaningful. We obtain some results for the sequences of Catalan numbers and of some numbers and polynomials which are related to Catalan…
Moments of secular and inverse secular coefficients, averaged over random matrices from classical groups, are related to the enumeration of non-negative matrices with prescribed row and column sums. Similar random matrix averages are…
There is a deep connection between the ground states of transverse-field spin systems and the late-time distributions of evolving viral populations -- within simple models, both are obtained from the principal eigenvector of the same…
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…
We introduce a class of linear bounded invertible operators on Banach spaces, called shift operators, which comprises weighted backward shifts and models finite products of weighted backward shifts and dissipative composition operators. We…
We prove that vertex-reinforced random walk on the integers with weight of order k to the power alpha, for alpha in [0, 1/2), is recurrent. This confirms a conjecture of Volkov for alpha<1/2. The conjecture for alpha in [1/2, 1) remains…
A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space $\mathcal{H}$ is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group $G$ on…