Related papers: A Formula for Inserting Point Masses

We study the asymptotic behavior of Markov operators $P_\mu$ defined by convolution with a probability measure $\mu$ on the unit circle $\mathbb T$. We prove that when $\mu$ is adapted, $P_\mu$ satisfies Doeblin's condition if and only if…

An improved volume-weighted probability measure for eternal inflation is proposed. For the models studied in this paper it leads to simple and intuitively expected gauge-invariant results.

We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a N x K…

Let $(X, \mathcal{B}, \mu)$ be a probability measure space and $T_1$, $T_2$, $T_3$ three not necessarily commuting measure preserving transformations on $(X, \mathcal{B}, \mu)$. We prove that for all bounded functions $f_1$, $f_2$, $f_3$…

We construct a probability measure $\mu$ supported on a set of zero $2d/p$-Hausdorff measure such that $\hat{\mu}\in L_{p}(\mathbb{R}^d)$.

A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…

We initiate a systematic investigation of group actions on compact medain algebras via the corresponding dynamics on their spaces of measures. We show that a probability measure which is invariant under a natural push forward operation must…

Let $\mu$ be an even Borel probability measure on ${\mathbb R}$. For every $N>n$ consider $N$ independent random vectors $\vec{X}_1,\ldots ,\vec{X}_N$ in ${\mathbb R}^n$, with independent coordinates having distribution $\mu $. We establish…

This paper proves that if points $Z_1,Z_2,...$ are chosen independently and identically using some measure $\mu$ from the unit circle in the complex plane, with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, then the empirical distribution of the…

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…

We present simple analytical approximations to matter-effect corrected effective neutrino mixing-angles and effective mass-squared-differences. The expressions clarify the dependence of oscillation probabilities in matter to the mixing…

Let $(X,{\mathcal A},\mu)$ be a probability space and let $S\colon X\to X$ be a measurable transformation. Motivated by the paper of K. Nikodem [Czechoslovak Math. J. 41(116) (4) (1991) 565--569], we concentrate on a functional equation…

Being motivated by general interest as well as by certain concrete problems of Fourier Analysis, we construct analogs of the Lp spaces for measures. It turns out that most of standard properties of the usual Lp spaces for functions are…

The loop measure is associated with a Markov generator. We compute the variation of the loop measure induced by an in nitesimal variation of the generator a ecting the killing rates or the jumping rates.

We study fast approximation of integrals with respect to stationary probability measures associated to iterated functions systems on the unit interval. We provide an algorithm for approximating the integrals under certain conditions on the…

We study the moment space corresponding to matrix measures on the unit circle. Moment points are characterized by non-negative definiteness of block Toeplitz matrices. This characterization is used to derive an explicit representation of…

We show that probability measures on the unit circle associated with Verblunsky coefficients obeying a Coulomb-type decay estimate have no singular continuous component.

We study the dynamics of polynomial-like mappings in several variables. A special case of our results is the following theorem. Let f be a proper holomorphic map from an open set U onto a Stein manifold V, $U\subset\subset V$. Assume f is…

We introduce a new formulation for differential equation describing dynamics of measures on an Euclidean space, that we call Measure Differential Equations with sources. They mix two different phenomena: on one side, a transport-type term,…

We construct a neutrino mass matrix $M_{\nu}$ via a seesaw mechanism whith perturbed invariant under a cyclic permutation by introducing one parameter $\delta$ into the diagonal elements of $M_{\nu}$ with assumption that trace of the…