Related papers: Interpretations of some parameter dependent genera…
We introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
Probability Distributions Functions (PDFs) of fluctuations of plasma edge parameters are skewed curves fairly different from normal distributions, whose shape appears almost independent of the plasma conditions and devices. We start from a…
We study the uncertainties of quantum mechanical observables, quantified by the standard deviation (square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions (PDFs) of the…
Representing the parton distribution functions (PDFs) of the proton and other hadrons through flexible, high-fidelity parametrizations has been a long-standing goal of particle physics phenomenology. This is particularly true since the…
The probability density function (PDF) of some global average quantity plays a fundamental role in critical and highly correlated systems. We explicitly compute this quantity as a function of the magnetization for the two dimensional XY…
Given a sample of independent and identically distributed random variables, a novel nonparametric maximum entropy method is presented to estimate the underlying continuous univariate probability density function (pdf). Estimates are found…
For the orthogonal-unitary and symplectic-unitary transitions in random matrix theory, the general parameter dependent distribution between two sets of eigenvalues with two different parameter values can be expressed as a quaternion…
The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings \beta = 1,2 and 4. It has been known for some time that there is an…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
A method providing optimal estimate of probability density functions (PDFs) from time series is proposed. It allows almost arbitrary resolution PDFs when applied to either, sampled analytic functions or digitized data from experiments. When…
We compute the uniform probability that finitely many polynomials over a finite field are pairwise coprime and compare the result with the formula one gets using the natural density as probability measure. It will turn out that the formulas…
We demonstrate the convergence of the characteristic polynomial of several random matrix ensembles to a limiting universal function, at the microscopic scale. The random matrix ensembles we treat are classical compact groups and the…
There exists an entire family of universal PDFs of the magnetization mode of the three dimensional Ising model parameterized by $\zeta = \lim_{L,\xi_{\infty}}L/\xi_{\infty}$ which is the ratio of the system size $L$ to the bulk correlation…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
We derive relations between polarized transverse momentum dependent distribution functions (TMDs) and the usual parton distribution functions (PDFs) in the 3D covariant parton model, which follow from Lorentz invariance and the assumption…
The work described in this paper can be interpreted as an application of the order patterns of symbolic dynamics when dealing with unimodal maps. Specifically, it is shown how Gray codes can be used to estimate the probability distribution…
The evolution of a quantum system, appropriate to describe nano-magnets, can be mapped on a Markov process, continuous in $\beta$. The mapping implies a probability assignment that can be used to study the probability density (PDF) of the…
A probability density function (PDF) of a spatially dependent field provides a means of calculating moments of the field or, equivalently, the proportion of a spatial domain that is mapped to a given set of values. This paper describes a…
Common practice in modern machine learning involves fitting a large number of parameters relative to the number of observations. These overparameterized models can exhibit surprising generalization behavior, e.g., ``double descent'' in the…