Related papers: Excess and Deficiency of Extreme Multidimensional …
The density of states for the Schroedinger equation with a Gaussian random potential is calculated in a space of dimension d=4-epsilon in the entire energy range including the vicinity of a mobility edge. Leading terms in 1/epsilon are…
This paper derives new bounds on the difference of the entropies of two discrete random variables in terms of the local and total variation distances between their probability mass functions. The derivation of the bounds relies on maximal…
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step $\Delta t$, and a…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
We derive a message passing method for computing the spectra of locally tree-like networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
It is shown that in the complex trajectory representation of quantum mechanics, the Born's Psi^{\star}\Psi probability density can be obtained from the imaginary part of the velocity field of particles on the real axis. Extending this…
In this article, the exponentiated discrete Lindley distribution is presented and studied. Some important distributional properties are discussed. Using the maximum likelihood method, estimation of the model parameters is investigated.…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
The energy of an elastic manifold in a random landscape at T=0 is shown numerically to obey a probability distribution that depends on size of the box it is put into. If the extent of the spatial fluctuations of the manifold is much less…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously…
The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not…
In the present paper a behavior of the "average case" approximation complexity for d-parametric random fields of tensor-type is studied. It was shown in [Lifshits and Tulyakova, 2006] that for a given approximation accuracy level the…
The standard deviations of the energy and Poynting power densities for an isotropic random field near a perfectly conducting planar boundary are characterized, based on quartic plane-wave expansions. For normal and transverse components,…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…