Related papers: CDF of non-central $\chi^2$ distribution revisited…
The Heckman-Opdam hypergeometric functions of type BC extend classical Jacobi functions in one variable and include the spherical functions of non-compact Grassmann manifolds over the real, complex or quaternionic numbers. There are various…
In this paper, the sum of L independent but not necessarily identically distributed (i.n.i.d.) extended $\eta$-$\mu$ variates is considered. In particular, novel expressions for the probability density function and cumulative distribution…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
The calculation of work distributions in a quantum many-body system is of significant importance and also of formidable difficulty in the field of nonequilibrium quantum statistical mechanics. To solve this problem, inspired by…
For large dimensional non-Hermitian random matrices $X$ with real or complex independent, identically distributed, centered entries, we consider the fluctuations of $f(X)$ as a matrix where $f$ is an analytic function around the spectrum of…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
An approximation, in the sense of $\Gamma$-convergence and in any dimension $d\geq1$, of Griffith-type functionals, with $p-$growth ($p>1$) in the symmetrized gradient, is provided by means of a sequence of non-local integral functionals…
Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. They possess very strong regularity properties (reminiscent of the regularity…
A graphical expansion formula for non-commutative matrix integrals with values in a finite-dimensional real or complex von Neumann algebra is obtained in terms of ribbon graphs and their non-orientable counterpart called Moebius graphs. The…
We present marginal cumulative distribution functions (CDF) for density matrices $\rho$ of fixed purity $\tfrac{1}{N}\le\mu_N(\rho)=\textrm{Tr}[\rho^2]\le 1$ for arbitrary dimension $N$. We give closed form analytic formulas for the cases…
For a holomorphic function f on a complex manifold M we explain in this article that the distribution associated to |f | 2$\alpha$ (Log|f | 2) q f --N by taking the corresponding limit on the sets {|f | $\ge$ $\epsilon$} when $\epsilon$…
The unpolarized spin-flip isoscalar generalized parton distribution function (E^u+E^d)(x,xi,t) is studied in the large-Nc limit at a low normalization point in the framework of the chiral quark-soliton model. This is the first study of…
We introduce a new pair of mutually dual bases of noncommutative symmetric functions and quasi-symmetric functions, and use it to derive generalizations of several results on the reduced incidence algebra of the lattice of noncrossing…
In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…
Fully differential heavy quark contributions to the photon structure functions in deeply inelastic scattering are computed in next-to-leading order QCD, including both the direct and resolved contributions. A variety of distributions are…
This paper extends Edgeworth-Cornish-Fisher expansions for the distribution and quantiles of nonparametric estimates in two ways. Firstly it allows observations to have different distributions. Secondly it allows the observations to be…
In the 1980's, Greene defined {\it hypergeometric functions over finite fields} using Jacobi sums. The framework of his theory establishes that these functions possess many properties that are analogous to those of the classical…
We classify the $Q$-homogeneous skew Schur $Q$-functions, i.e., those of the form $Q_{\lambda/\mu} = k \cdot Q_{\nu}$. On the way we develop new tools that are useful also in the context of other classification problems for skew Schur…
We consider the generic nonanticommutative model of chiral-antichiral superfields on ${\cal N}={1\over 2}$ superspace. The model is formulated in terms of an arbitrary K\"ahlerian potential, chiral and antichiral superpotentials and can…
The cumulants and moments of the log of the non-central chi-square distribution are derived. For example, the expected log of a chi-square random variable with v degrees of freedom is log(2) + psi(v/2). Applications to modeling probability…