Related papers: Absolute continuity and singularity of two probabi…

Exploiting a construction of rigidity sequences for weakly mixing dynamical systems by Fayad and Thouvenot, we show that for every integers $p_{1},\dots,p_{r}$ there exists a continuous probability measure $\mu $ on the unit circle…

Let $\mu$ = ($\mu$t)t$\in$R be a 1-parameter family of probability measures on R. In [11] we introduced its ``Markov-quantile''process: a process X= (Xt)t$\in$R that resembles as much as possible the quantile process attached to $\mu$,…

Let $\nu$ be a finite complex measure with support in $\bar {\mathbb D}$ and let $\mathcal C\nu$ denote the Cauchy transform of $\nu .$ Suppose that $\nu$ annihilates polynomials in complex variable $z$ and $\nu |_{\partial \mathbb D} =…

Let $\mu$ and $\nu$ be two Borel probability measures on two separable metric spaces $\X$ and $\Y$ respectively. For $h, g$ be two Hausdorff functions and $q\in \R$, we introduce and investigate the generalized pseudo-packing measure…

Separability conditions for a bipartite quantum system of finite-dimensional subsystems are formulated in terms of R\'{e}nyi and Tsallis entropies. Entropic uncertainty relations often lead to entanglement criteria. We propose new approach…

Picture an experimental scenario where a closed quantum system, evolving through a time-independent Hamiltonian, is subject to a demolition measurement at a chosen time. The Hamiltonian, the measured observables, the initial state of the…

Consider a totally irregular measure $\mu$ in $\mathbb{R}^{n+1}$, that is, the upper density $\limsup_{r\to0}\frac{\mu(B(x,r))}{(2r)^n}$ is positive $\mu$-a.e.\ in $\mathbb{R}^{n+1}$, and the lower density…

One can consider $\mu$-Martin-L\"of randomness for a probability measure $\mu$ on $2^{\omega}$, such as the Bernoulli measure $\mu_p$ given $p \in (0, 1)$. We study Bernoulli randomness of sequences in $n^{\omega}$ with parameters $p_0,…

We let U=SU(2) and K=SO(2) and denote N_{U}(K) the normalizer of K in U. For a an element of U\ N_{U} (K), we let \mu_{a} be the normalized singular measure supported in KaK. For p a positive integer, it was proved that \mu_{a}^{( p)}, the…

Yanni Chen extended the classical Beurling-Helson-Lowdenslager Theorem for Hardy spaces on the unit circle $\mathbb{T}$ defined in terms of continuous gauge norms on $L^{\infty}$ that dominate $\Vert\cdot\Vert_{1}$. We extend Chen's result…

The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses…

The Hilbert space $\mathcal H$ of backward renormalisation of an anyonic quantum spin chain affords a unitary representation of Thompson's group $F$ via local scale transformations. Given a vector in the canonical dense subspace of…

The aim of the MuCap experiment is a 1% measurement of the singlet capture rate Lambda_S for the basic electro-weak reaction mu + p -> n + nu_mu. This observable is sensitive to the weak form-factors of the nucleon, in particular to the…

We investigate generalized measurements, based on positive-operator-valued measures, and von Neumann measurements for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. In particular, we…

Let $\mu$ be a probability measure on $\mathbb{R}$. We give conditions on the Fourier transform of its density for functionals of the form $H(a)=\int_{\mathbb{R}^n}h(\langle a,x\rangle)\mu^n(dx)$ to be Schur monotone. As applications, we…

The halfspace depth of a $d$-dimensional point $x$ with respect to a finite (or probability) Borel measure $\mu$ in $\mathbb{R}^d$ is defined as the infimum of the $\mu$-masses of all closed halfspaces containing $x$. A natural question is…

We note an elementary proof of the existence and uniqueness of a solution $% \mu \in \mathbb{P(X)}$ to the equation $\mu =p\mu_{0}+q\hat{F}\mu $. Here $\mathbb{X}$ is a topological space, $\mathbb{P(X)}$ is the set of Borel measures of unit…

In [12], we proved that $1$-d periodic fractional Schr\"odinger equation with cubic nonlinearity is locally well-posed in $H^s$ for $s>\frac{1-\alpha}{2}$ and globally well-posed for $s>\frac{5\alpha-1}{6}$. In this paper we define an…

Consider a measure $\mu$ on $\R^n$ generating a natural exponential family $F(\mu)$ with variance function $V_{F(\mu)}(m)$ and Laplace transform $$ \exp(\ell_{\mu}(s))=\int_{\R^n} \exp(-\<s,x\>)\mu(dx).$$ A dual measure $\mu^*$ satisfies…

We study the fixed point for a non-linear transformation in the set of Hausdorff moment sequences, defined by the formula: $T((a_n))_n=1/(a_0+... +a_n)$. We determine the corresponding measure $\mu$, which has an increasing and convex…