Related papers: Singular Schaeffer-Salem measures of dynamical sys…
Green, Tao and Ziegler prove ``Dense Model Theorems'' of the following form: if R is a (possibly very sparse) pseudorandom subset of set X, and D is a dense subset of R, then D may be modeled by a set M whose density inside X is…
In this note, we shall consider the existence of invariant measures for a class of infinite dimensional stochastic functional differential equations with delay whose driving semigroup is eventually norm continuous. The results obtained are…
It is generally believed that dispersive polarimetric detection of collective angular momentum in large atomic spin systems gives rise to: squeezing in the measured observable, anti-squeezing in a conjugate observable, and collective spin…
In this note, we investigate $C^2$ differential images of the homogeneous self-similar measure associated with an IFS $\mathcal{I}=\{\rho x+a_j\}_{j=1}^m$ satisfying the strong separation condition and a positive probability vector…
A test of uniformity on [0,1] is developed for the setting of a single observation recorded with sufficient precision. Although consistency against general alternatives is not attainable with only one draw in the classical large-sample…
We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random…
Novel results for the self-consistent single-particle spectral function and self-energy are presented for non-degenerate one-component Coulomb systems at various densities and temperatures. The GW^0-method for the dynamical self-energy is…
In this paper we start studying spectral properties of the Fourier-Stieltjes algebras, largely following Zafran's work on the algebra of measures on a locally compact group. We show that for a large class of discrete groups the Wiener-Pitt…
We study spectra of Schr\"odinger operators on $\RR^d$. First we consider a pair of operators which differ by a compactly supported potential, as well as the corresponding semigroups. We prove almost exponential decay of the singular values…
We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…
We show that the weak limit of the maximal measures for any degenerating sequence of rational maps on the Riemann sphere must be a countable sum of atoms. For a 1-parameter family f_t of rational maps, we refine this result by showing that…
We show that for Lebesgue almost all $d$-tuples $(\theta_1,\ldots,\theta_d)$, with $|\theta_j|>1$, any self-affine measure for a homogeneous non-degenerate iterated function system $\{Ax+a_j\}_{j=1}^m$ in ${\mathbb R}^d$, where $A^{-1}$ is…
We prove that every closed set which is not sigma-finite with respect to the Hausdorff measure H^{N-1} carries singularities of continuous vector fields in the Euclidean space R^N for the divergence operator. We also show that finite…
The torsional oscillator is the chief instrument for investigating supersolidity in solid 4He. These oscillators can be sensitive to the elastic properties of the solid helium, which show anomalies over the same range of temperature in…
Dynamical properties of uniform electron fluids (jellium model) are studied within a novel non-perturbative approach consisting in the combination of the self-consistent version of the method of moments (SCMM) involving up to nine sum rules…
In this paper we demonstrate that the weak temperature dependence of structure factor of supercooled liquids, a defining feature of the glass transition, is a consequence of the averaging of the scattering intensity either due to the use of…
We study uncertainty principles for function classes on the torus. The classes are defined in terms of spectral subspaces of the energy or the momentum, respectively. In our main theorems, the support of the Fourier transform of the…
Long-wavelength collective shear dynamics are profoundly different in solids and liquids. According to the theoretical framework developed by Maxwell and Frenkel, collective shear waves vanish upon melting by acquiring a characteristic…
Using tools from computable analysis we develop a notion of effectiveness for general dynamical systems as those group actions on arbitrary spaces that contain a computable representative in their topological conjugacy class. Most natural…
The purpose of this note is to investigate the high frequency behaviour of solutions to linear Schr\"odinger equations. More precisely, Bourgain and Anantharaman-Macia proved that any weak-* limit of the square density of solutions to the…