相关论文: Probability density function of the Cartesian x-co…
The one-point probability distribution function (PDF) of the matter density field in the universe is a fundamental property that plays an essential role in cosmology for estimates such as gravitational weak lensing, non-linear clustering,…
To complete a previous paper, the probability density functions of the center-of-gravity as positioning algorithm are derived with classical methods. These methods, as suggested by the textbook of Probability, require the preliminary…
In this manuscript we analyse the behaviour of the probability density function of the sum of $N$ deterministic variables generated from the triangle map of Casati-Prosen. For the case in which the map is both ergodic and mixing the…
Given $n$ independent random marked $d$-vectors $X_i$ with a common density, define the measure $\nu_n = \sum_i \xi_i $, where $\xi_i$ is a measure (not necessarily a point measure) determined by the (suitably rescaled) set of points near…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
This paper considers a multivariate spatial random field, with each component having univariate marginal distributions of the skew-Gaussian type. We assume that the field is defined spatially on the unit sphere embedded in $\mathbb{R}^3$,…
The Gaussian polytope $\mathcal P_{n,d}$ is the convex hull of $n$ independent standard normally distributed points in $\mathbb R^d$. We derive explicit expressions for the probability that $\mathcal P_{n,d}$ contains a fixed point…
The coordinates along any fixed direction(s), of points on the sphere $S^{n-1}(\sqrt{n})$, roughly follow a standard Gaussian distribution as $n$ approaches infinity. We revisit this classical result from a nonstandard analysis perspective,…
The probability distribution functions of the circulation of velocity in three-dimensional decaying isotropic turbulence are examined by the database of the numerical simulation based on the pseudospectral method. It is shown that the…
We are studying the problem of estimating density in a wide range of metric spaces, including the Euclidean space, the sphere, the ball, and various Riemannian manifolds. Our framework involves a metric space with a doubling measure and a…
To complete a previous work, the probability density functions for the errors in the center-of-gravity as positioning algorithm are derived with the usual methods of the cumulative distribution functions. These methods introduce substantial…
The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…
This paper derives central limit and bootstrap theorems for probabilities that sums of centered high-dimensional random vectors hit hyperrectangles and sparsely convex sets. Specifically, we derive Gaussian and bootstrap approximations for…
We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density…
Let $X$ be a $d$-dimensional random vector and $X_\theta$ its projection onto the span of a set of orthonormal vectors $\{\theta_1,...,\theta_k\}$. Conditions on the distribution of $X$ are given such that if $\theta$ is chosen according to…
Context: Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF). In order to successfully exploit such observables, a detailed…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
We investigate the form of the one-point probability distribution function (pdf) for the density field of the interstellar medium using numerical simulations that successively reduce the number of physical processes included.…
We present a new calculation for the evolution of the 1-point Probability Distribution Function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman-Kolmogorov equation and second-order Eulerian…
We calculate the one-point probability distribution function (PDF) for cosmic density in non-linear regime of the gravitational evolution. Under the local approximation that the evolution of cosmic fluid fields can be characterized by the…