Related papers: Generic measures with slowly decaying Fourier coef…
This paper introduces a novel extension of Fr\'{e}chet means, called \textit{generalized Fr\'{e}chet means} as a comprehensive framework for characterizing features in probability distributions in general topological spaces. The generalized…
We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…
Let $M$ be a closed manifold, and let $f:M \rightarrow M$ be a $C^{2+\alpha}$ Axiom A diffeomorphism. Suppose that $f$ has an attractor $\Omega$ with codimension 1 stable lamination. Under a generic nonlinearity condition and a suitable…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
We examine the constraints of spherically symmetric general relativity with one asymptotically flat region, exploiting both the traditional metric variables and variables constructed from the optical scalars. With respect to the latter…
For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…
A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice $\mathbb{Z}^{2}$, gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak…
The effect of Coulomb and short-range interactions on the spectral properties of two-dimensional disordered systems with two spinless fermions is investigated by numerical scaling techniques. The size independent universality of the…
While there exists a well-developed asymptotic theory of Fr\'echet means of random variables taking values in a general "finite-dimensional" metric space, there are only a few known results in which the random variables can take values in…
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon,…
We show that self-similar measures on $\mathbb{R}^d$ satisfying the weak separation condition are uniformly scaling. Our approach combines elementary ergodic theory with geometric analysis of the structure given by the weak separation…
We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random…
If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the…
A subshift with linear block complexity has at most countably many ergodic measures, and we continue of the study of the relation between such complexity and the invariant measures. By constructing minimal subshifts whose block complexity…
We extend the idea of weak measurements to the general case, provide a complete treatment and obtain results for both the regime when the pre-selected and post-selected states (PPS) are almost orthogonal and the regime when they are exactly…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks. The characterization is a true analogue of the Maxwell-Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial…
We show that any ergodic measure for a piecewise monotonic map with positive metric entropy is approximated by periodic measures in the weak-* sense. This partially answers Hofbauer-Raith's conjecture.
Recent quantum technologies utilize complex multidimensional processes that govern the dynamics of quantum systems. We develop an adaptive diagonal-element-probing compression technique that feasibly characterizes any unknown quantum…
Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low…