Related papers: Relativistic regularized kappa distributions
Numerical procedures for generating non-Maxwellian velocity distributions in particle simulations are presented. First, Monte Carlo methods for an $(r,q)$ distribution that generalizes flattop and kappa distributions are discussed. Then,…
This letter reports two moment extensions of the entropy of a distribution. By understanding the traditional entropy as the average of the original distribution up to a random variable transformation, the traditional moments equation become…
A semi-analytic method to compute the first coefficients of the renormalization group functions on a random lattice is introduced. It is used to show that the two-dimensional $O(N)$ non-linear $\sigma$-model regularized on a random lattice…
The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…
We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the…
The central limit theorem provides the theoretical foundation for the universality of the normal distribution: under broad conditions, the asymptotic distribution of a sum of independent random variables approaches a Gaussian. Yet, physical…
The envelope of an elliptical Gaussian complex vector, or equivalently, the amplitude or norm of a bivariate normal random vector has application in many weather and signal processing contexts. We explicitly characterize its distribution in…
Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…
From a suitable integral representation of the Laplace transform of a positive semi-definite quadratic form of independent real random variables with not necessarily identical densities a univariate integral representation is derived for…
We study minimization of a parametric family of relative entropies, termed relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}(P,Q)$). These arise as redundancies under mismatched compression when cumulants of compressed lengths are…
In the present effort we consider the most general non linear particle kinetics within the framework of the Fokker-Planck picture. We show that the kinetics imposes the form of the generalized entropy and subsequently we demonstrate the…
Accurate radiative transfer coefficients (emissivities, absorptivities, and rotativities) are needed for modeling radiation from relativistically hot, magnetized plasmas such as those found in Event Horizon Telescope sources. Here we…
We present a rigorous study of quantum diffusion of a relativistic particle subjected to a time-dependent random potential with $\delta$ correlation in time. We find that in the asymptotic time limit the particle wave packet spreads…
The low-temperature form of the equilibrium relativistic mass distribution is subject to the Galilean limit by taking $c\rightarrow \infty .$ In this limit the relativistic Maxwell-Boltzmann distribution passes to the usual nonrelativistic…
Normalizing flows, which learn a distribution by transforming the data to samples from a Gaussian base distribution, have proven powerful density approximations. But their expressive power is limited by this choice of the base distribution.…
Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. Kamiya, Takemura and Kuriki (2006) generalized the elliptically contoured…
Elliptically contoured distributions generalize the multivariate normal distributions in such a way that the density generators need not be exponential. However, as the name suggests, elliptically contoured distributions remain to be…
The damped and parametrically driven nonlinear Dirac equation with arbitrary nonlinearity parameter $\kappa$ is analyzed, when the external force is periodic in space and given by $f(x) =r\cos(K x)$, both numerically and in a variational…
We derive upper and lower limits for the basic physical parameters (mass-radius ratio, anisotropy, redshift and total energy) for arbitrary anisotropic general relativistic matter distributions in the presence of a cosmological constant.…
We investigate the distribution of critical points of certain isotropic random functions $\Phi$ on $\mathbb{R}^m$. We show that the distribution of critical points of $\Phi(Rx)$, suitably normalized, converge a.s. and $L^2$ as random…