Related papers: Hyperuniformity and hyperfluctuations of random me…
We consider an independent and identically distributed (i.i.d.) random dynamical system of simple linear transformations on the unit interval $T_{\beta}(x)=\beta x$ (mod $1$), $x\in[0,1]$, $\beta>0$, which are the so-called…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
We prove a model-theoretic representation theorem for the distribution of an ergodic exchangeable $k$-uniform hypergraph: every such measure arises as the pushforward of the countably-iterated Morley product of a global Borel-definable…
In this paper we deal with an invariant ergodic hyperbolic measure $\mu$ for a diffeomorphism $f,$ assuming that $f$ it is either $C^{1+\alpha}$ or $f$ is $C^1$ and the Oseledec splitting of $\mu$ is dominated. We show that this system…
Aim of this short note is to show that a dimension-free Harnack inequality on an infinitesimally Hilbertian metric measure space where the heat semigroup admits an integral representation in terms of a kernel is suffcient to deduce a sharp…
We prove that every hyperbolic measure invariant under a C^{1+\alpha} diffeomorphism of a smooth Riemannian manifold possesses asymptotically ``almost'' local product structure, i.e., its density can be approximated by the product of the…
We analyze entropic uncertainty relations for two orthogonal measurements on a $N$-dimensional Hilbert space, performed in two generic bases. It is assumed that the unitary matrix $U$ relating both bases is distributed according to the Haar…
We define spherical diffraction measures for a wide class of weighted point sets in commutative spaces, i.e. proper homogeneous spaces associated with Gelfand pairs. In the case of the hyperbolic plane we can interpret the spherical…
Hyperuniform point patterns are characterized by vanishing infinite wavelength density fluctuations and encompass all crystal structures, certain quasi-periodic systems, and special disordered point patterns. This article generalizes the…
We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random…
Elements of a novel theory of quantum physics are developed, synthesising the role of symbolism in describing quantum measurement and in the topological representation of fractal invariant sets in nonlinear dynamical systems theory. In this…
We characterize Gaussian estimates for transition probability of a discrete time Markov chain in terms of geometric properties of the underlying state space. In particular, we show that the following are equivalent: (1) Two sided Gaussian…
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
Bargmann invariants, multivariate traces of states, completely characterize any unitary-invariant property of a set of states. Unitary invariants enable the description of quantum resources such as basis-independent coherence and…
We introduce a rigorous and sensitive significance test for hyperuniformity that yields reliable results even from a single sample. Our approach is based on a detailed analysis of the empirical Fourier transform of a stationary point…
In this paper, we explore spectral measures whose square integrable spaces admit a family of exponential functions as an orthonormal basis.Our approach involves utilizing the integral periodic zeros set of Fourier transform to characterize…
Two new omnibus tests of uniformity for data on the hypersphere are proposed. The new test statistics exploit closed-form expressions for orthogonal polynomials, feature tuning parameters, and are related to a "smooth maximum" function and…
We consider consistent diffusion dynamics, leaving the celebrated Hua-Pickrell measures, depending on a complex parameter $s$, invariant. These, give rise to Feller-Markov processes on the infinite dimensional boundary $\Omega$ of the…