Related papers: Correlations with tailored extremal properties
Two of the most intriguing features of quantum physics are the uncertainty principle and the occurrence of nonlocal correlations. The uncertainty principle states that there exist pairs of incompatible measurements on quantum systems such…
Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail…
We study first and second order coherence of trapped dilute Bose gases using appropriate correlation functions. Special attention is given to the discussion of second order or density correlations. Except for a small region around the…
Nonclassical properties of correlations-- like unpredictability, no-cloning and uncertainty-- are known to follow from two assumptions: nonlocality and no-signaling. For two-input-two-output correlations, we derive these properties from a…
We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation…
Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…
We present a new approach to study measures on ensembles of contours, polymers or other objects interacting by some sort of exclusion condition. For concreteness we develop it here for the case of Peierls contours. Unlike existing methods,…
How can we characterize different types of correlation between quantum systems? Since correlations cannot be generated locally, we take any real function of a multipartite state which cannot increase under local operations to measure a…
Extreme values modeling has attracting the attention of researchers in diverse areas such as the environment, engineering, or finance. Multivariate extreme value distributions are particularly suitable to model the tails of multidimensional…
We define some natural notions of strong and weak Borel Ramsey properties for countable Borel equivalence relations and show that they hold for a countable Borel equivalence relation if and only if the equivalence relation is smooth. We…
Azadkia and Chatterjee (2021) recently introduced a simple nearest neighbor (NN) graph-based correlation coefficient that consistently detects both independence and functional dependence. Specifically, it approximates a measure of…
This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixtures that we propose of Pearson's and…
We present a characterization of the set of non-signaling correlations in terms of a two dimensional representation that involves the maximal value of a Bell functional and the mutual information between the parties. In particular, we apply…
The coefficient of determination is well defined for linear models and its extension is long wanted for mixed-effects models. We revisit its extension to define measures for proportions of variation explained by the whole model, fixed…
We are interested in the problem of characterizing the correlations that arise when performing local measurements on separate quantum systems. In a previous work [Phys. Rev. Lett. 98, 010401 (2007)], we introduced an infinite hierarchy of…
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…
Correlations in Bell and noncontextuality inequalities can be expressed as a positive linear combination of probabilities of events. Exclusive events can be represented as adjacent vertices of a graph, so correlations can be associated to a…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…
Quantum theory predicts and experiments confirm that nature can produce correlations between distant events that are nonlocal in the sense of violating a Bell inequality. Nevertheless, Bell's strong sentence {\it Correlations cry out for…
Calling the quantity; 2delta(A)delta(B)/|<[A, B]>|, with non-zero denominator, the uncertainty product ratio or UPR for the pair of observables, (A, B), it is shown that any non-zero correlation coefficient between two observables raises,…