Search results for "Cumulant"
showing 10 items of 20 documents
Meaning and magnitude of the reduced density matrix cumulants
2012
Abstract Within the framework of a generalized normal ordering (GNO), invented by Mukherjee [1] , the reduced density matrix cumulants of the (multiconfigurational) reference wave function play a central role, as they arise directly from the contraction rules. The extended Wick theorem allows contractions of an arbitrary number of active annihilators and creators through a cumulant of corresponding rank. Because the cumulant rank truncates naturally only at the number of active spin orbitals, practical applications of the GNO concept seem to rely on a fast convergence of the cumulant series, allowing one to neglect cumulants with high rank. By computing cumulant norms for selected systems (…
Correlated gluonic hot spots meet symmetric cumulants data at LHC energies
2019
We present a systematic study on the influence of spatial correlations between the proton constituents, in our case gluonic hot spots, their size and their number on the symmetric cumulant SC(2, 3), at the eccentricity level, within a Monte Carlo Glauber framework [1]. When modeling the proton as composed by 3 gluonic hot spots, the most common assumption in the literature, we find that the inclusion of spatial correlations is indispensable to reproduce the negative sign of SC(2, 3) in the highest centrality bins as dictated by data. Further, the subtle interplay between the different scales of the problem is discussed. To conclude, the possibility of feeding a 2+1D viscous hydrodynamic sim…
A method for the probabilistic analysis of nonlinear systems
1995
Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…
Sampling properties of the Bayesian posterior mean with an application to WALS estimation
2022
Many statistical and econometric learning methods rely on Bayesian ideas, often applied or reinterpreted in a frequentist setting. Two leading examples are shrinkage estimators and model averaging estimators, such as weighted-average least squares (WALS). In many instances, the accuracy of these learning methods in repeated samples is assessed using the variance of the posterior distribution of the parameters of interest given the data. This may be permissible when the sample size is large because, under the conditions of the Bernstein--von Mises theorem, the posterior variance agrees asymptotically with the frequentist variance. In finite samples, however, things are less clear. In this pa…
Searching for a hidden sector in multiparticle production at LHC
2016
A hidden sector beyond the Standard Model can show up in multiparticle production altering inclusive correlations and factorial cumulants of multiplicity distributions. In this report such a study is advocated with a special emphasis on the searches at LHC.
Two-Dimensional Melting Approached via Finite-Size Scaling of Bond-Orientational Order
1994
Relying on Monte Carlo simulations, we investigate the hard-disk melting transition. The finite-size scaled values of the bond-orientational order parameter moments are obtained with the block analysis technique. The behaviour of Binder's cumulant and the susceptibility favour an interpretation in terms of a first-order transition.
New analytical approach to analyze the nonlinear regime of stochastic resonance
2015
We propose some approximate methods to explore the nonlinear regime of the stochastic resonance phenomenon. These approximations correspond to different truncation schemes of cumulants. We compare the theoretical results for the signal power amplification, obtained by using ordinary cumulant truncation schemes, that is Gaussian and excess approximations, the modified two-state approximation with those obtained by numerical simulations of the Langevin equation describing the dynamics of the system.
Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables
2012
Abstract The aim of this paper is the probabilistic representation of the probability density function (PDF) or the characteristic function (CF) in terms of fractional moments of complex order. It is shown that such complex moments are related to Riesz and complementary Riesz integrals at the origin. By invoking the inverse Mellin transform theorem, the PDF or the CF is exactly evaluated in integral form in terms of complex fractional moments. Discretization leads to the conclusion that with few fractional moments the whole PDF or CF may be restored. Application to the pathological case of an α -stable random variable is discussed in detail, showing the impressive capability to characterize…
Searching for hidden sectors in multiparticle production at the LHC
2016
Most signatures of new physics in colliders have been studied so far on the transverse plane with respect to the beam direction. In this work however we study the impact of a hidden sector beyond the Standard Model (SM) on inclusive (pseudo)rapidity correlations and moments of the multiplicity distributions, with special emphasis in the LHC results.
Multi-particle azimuthal correlations in p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider
2014
Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the prese…