1,447,495 research outputs found
Measuring and testing dependence by correlation of distances
Distance correlation is a new measure of dependence between random vectors.
Distance covariance and distance correlation are analogous to product-moment
covariance and correlation, but unlike the classical definition of correlation,
distance correlation is zero only if the random vectors are independent. The
empirical distance dependence measures are based on certain Euclidean distances
between sample elements rather than sample moments, yet have a compact
representation analogous to the classical covariance and correlation.
Asymptotic properties and applications in testing independence are discussed.
Implementation of the test and Monte Carlo results are also presented.Comment: Published in at http://dx.doi.org/10.1214/009053607000000505 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Long-distance asymptotic behaviour of multi-point correlation functions in massless quantum models
We provide a microscopic model setting that allows us to readily access to
the large-distance asymptotic behaviour of multi-point correlation functions in
massless, one-dimensional, quantum models. The method of analysis we propose is
based on the form factor expansion of the correlation functions and does not
build on any field theory reasonings. It constitutes an extension of the
restricted sum techniques leading to the large-distance asymptotic behaviour of
two-point correlation functions obtained previously.Comment: 25 page
Estimation of Distance Correlation: a Simulation-based Comparative Study
Cursos e Congresos, C-155[Abstract] The notion of distance correlationwas introduced to measure the dependence between
two random vectors, not necessarily of equal dimensions, in a multivariate setting. In their work,
Sz´ekely et al. (2007) proposed an estimator for the squared distance covariance, and they also
proved that this estimator is a V-statistic. On the other hand, Sz´ekely and Rizzo (2014) introduced
an unbiased version of the squared sample distance covariance, which was subsequently
identified as a U-statistic in Huo and Sz´ekely (2016). In this study, a simulation is conducted to
compare both distance correlation estimators: the U-estimator and the V-estimator. The analysis
assesses their efficiency (mean squared error) and contrasts the computational times of both
approaches across various dependence structuresCITIC is funded by the Xunta de Galicia through the collaboration agreement between the Conseller
´ıa de Cultura, Educaci´on, Formaci´on Profesional e Universidades and the Galician universities
for the reinforcement of the research centres of the Galician University System (CIGUS
Quantifying quantum coherence and non-classical correlation based on Hellinger distance
Quantum coherence and non-classical correlation are key features of quantum
world. Quantifying coherence and non-classical correlation are two key tasks in
quantum information theory. First, we present a bona fide measure of quantum
coherence by utilizing the Hellinger distance. This coherence measure is proven
to fulfill all the criteria of a well defined coherence measure, including the
strong monotonicity in the resource theories of quantum coherence. In terms of
this coherence measure, the distribution of quantum coherence in multipartite
systems is studied and a corresponding polygamy relation is proposed. Its
operational meanings and the relations between the generation of quantum
correlations and the coherence are also investigated. Moreover, we present
Hellinger distance-based measure of non-classical correlation, which not only
inherits the nice properties of the Hellinger distance including contractivity,
and but also shows a powerful analytic computability for a large class of
quantum states. We show that there is an explicit trade-off relation satisfied
by the quantum coherence and this non-classical correlation
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