Related papers: On Asymptotically Orthonormal Sequences
We prove that the number of copies of any given permutation pattern $q$ has an asymptotically normal distribution in random permutations.
Motivated by novel results in the theory of black-hole quantization, we study {\it analytically} the quasinormal modes (QNM) of ({\it rotating}) Kerr black holes. The black-hole oscillation frequencies tend to the asymptotic value…
We take a random matrix theory approach to random sketching and show an asymptotic first-order equivalence of the regularized sketched pseudoinverse of a positive semidefinite matrix to a certain evaluation of the resolvent of the same…
We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The…
Aperiodic autocorrelation is an important indicator of performance of sequences used in communications, remote sensing, and scientific instrumentation. Knowing a sequence's autocorrelation function, which reports the autocorrelation at…
We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations.…
Let $\mathscr{I}$ be an ideal sheaf on $P^n$ defining a subscheme $X$. Associated to $\mathscr{I}$ there are two elementary invariants: the invariant $s$ which measures the positivity of $\mathscr{I}$, and the minimal number $d$ such that…
Morphic sequences form a natural class of infinite sequences, typically defined as the coding of a fixed point of a morphism. Different morphisms and codings may yield the same morphic sequence. This paper investigates how to prove that two…
Integer partitions have fascinated people for centuries, from Ramanujan's groundbreaking congruences to the modern theory of modular forms. This paper investigates the statistical properties of odd unimodal sequences--a natural refinement…
While $(2+1)$-dimensional black holes in the Einstein theory allow for only the anti-de Sitter asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter and anti-de Sitter cases are included. Here we…
In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix…
Sequential tests and their implied confidence sequences, which are valid at arbitrary stopping times, promise flexible statistical inference and on-the-fly decision making. However, strong guarantees are limited to parametric sequential…
The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrodinger-like equation to the complex plane and then performing a method of monodromy matching at the…
We compute the spectrum of quasinormal frequencies of regular black holes obtained in the presence of Non-Linear Electrodynamics. In particular, we perturb the black hole with a minimally coupled massive scalar field, and we study the…
A stationary Poisson line tessellation is considered whose directional distribution is concentrated on two different atoms with some positive weights. The shape of the typical cell of such a tessellation is studied when its area or its…
A continuous-time dynamical system with parameter $\varepsilon$ is nearly-periodic if all its trajectories are periodic with nowhere-vanishing angular frequency as $\varepsilon$ approaches 0. Nearly-periodic maps are discrete-time analogues…
We study Krasnoselskii-Mann style iterative algorithms for approximating fixpoints of asymptotically weakly contractive mappings, with a focus on providing generalised convergence proofs along with explicit rates of convergence. More…
Let $(\omega, A_E)$ be a quasi-periodic Schr\"odinger cocycle, where $\omega$ is a Diophantine irrational. The potential is assumed to be $C^2$ with a unique non-degenerate minimum, and the coupling constant is assumed to be large. We show…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…