Related papers: Scott functions, their representations on domains,…
The trajectories of diffusion processes are continuous but non-differentiable, and each occurs with vanishing probability. This introduces a gap between theory, where path probabilities are used in many contexts, and experiment, where only…
This paper studies the local structure of continuous random fields on $\mathbb R^d$ taking values in a complete separable linear metric space ${\mathbb V}$. Extending seminal work of Falconer, we show that the generalized $(1+k)$-th order…
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an…
The notion of random sequence was introduced by Martin-Loef in 1966. At the same time he defined the so-called randomness deficiency function that shows how close are random sequences to non-random (in some natural sense). Other deficiency…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
The study of properties of mean functionals of random probability measures is an important area of research in the theory of Bayesian nonparametric statistics. Many results are now known for random Dirichlet means, but little is known,…
We recall the physical features of the parton distributions in the quantum statistical approach of the nucleon, which allows to describe simultaneously, unpolarized and polarized Deep Inelastic Scattering data. Some predictions from a…
The theory of influences in product measures has profound applications in theoretical computer science, combinatorics, and discrete probability. This deep theory is intimately connected to functional inequalities and to the Fourier analysis…
Covariance functions are the core of spatial statistics, stochastic processes, machine learning as well as many other theoretical and applied disciplines. The properties of the covariance function at small and large distances determine the…
We present results for Choquet integrals with minimal assumptions on the monotone set function through which they are defined. They include the equivalence of sublinearity and strong subadditivity independent of regularity assumptions on…
We consider square-integrable functionals of Poisson point processes for which the variance upper bound provided by the classical Poincar\'{e} inequality is suboptimal, a phenomenon known as superconcentration. In this paper, we establish a…
About forty years ago it was realized by several researchers that the essential features of certain objects of Probability theory, notably Gaussian processes and limit theorems, may be better understood if they are considered in settings…
Distribution function is essential in statistical inference, and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates…
The advent of the Hohenberg-Kohn theorem in 1964, its extension to finite-T, Kohn-Sham theory, and relativistic extensions provide the well-established formalism of density-functional theory (DFT). This theory enables the calculation of all…
Particle number fluctuations, no matter how small, are present in experimental set-ups. One should rigorously take these fluctuations into account, especially, for entanglement detection. In this context, we generalize the spin squeezing…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
For distribution regression problem, where a bag of $x$--observations is mapped to a single $y$ value, a one--step solution is proposed. The problem of random distribution to random value is transformed to random vector to random value by…
We introduce the semiclassical Wehrl entropy for the nucleon as a measure of complexity of the multiparton configuration in phase space. This gives a new perspective on the nucleon tomography. We evaluate the entropy in the small-$x$ region…