Related papers: A strong FKG inequality for multiple events
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
This work deals with the Mann's stochastic iteration algorithm under strong mixing random errors. We establish the Fuk-Nagaev's inequalities that enable us to prove the almost complete convergence with its corresponding rate of convergence.…
In this paper, the concept of the classical $f$-divergence (for a pair of measures) is extended to the mixed $f$-divergence (for multiple pairs of measures). The mixed $f$-divergence provides a way to measure the difference between multiple…
We analyze the well-posedness of a so called McKean Feynman-Kac Equation (MFKE), which is a McKean type equation with a Feynman-Kac perturbation. We provide in particular weak and strong existence conditions as well as pathwise uniqueness…
In this short note, we find an equivalent combinatorial condition only involving finite sums under which a centered Gaussian random vector with multinomial covariance matrix satisfies the Gaussian product inequality (GPI) conjecture. These…
In this note we investigate correlation inequalities for `up-sets' of permutations, in the spirit of the Harris--Kleitman inequality. We focus on two well-studied partial orders on $S_n$, giving rise to differing notions of up-sets. Our…
Postselection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the postselected events can give rise to anomalous values lying outside the spectrum of the measured…
We investigate the multiparticle quantum superposition and the persistence of multipartite entanglement of the quantum superposition generated by the quantum injected high-gain optical parametric amplification of a single photon. The…
The evaluation of the probability of union of a large number of independent events requires several combinations involving the factorial and the use of high performance computers with several hours of processing. Bounds and simplifications…
We develop a rigorous connection between statistical properties of an interference pattern and the coherence properties of the underlying quantum state. With explicit examples, we demonstrate that even for inaccurate reconstructions of…
We establish a sharp moment comparison inequality between an arbitrary negative moment and the second moment for sums of independent uniform random variables, which extends Ball's cube slicing inequality.
We provide a generalized definition of polygamy relations for any quantum correlation measures. Instead of the usual polygamy inequality, a polygamy relation with equality is given by introducing the polygamy weight. From the polygamy…
Let K be a field of positive characteristic. When V is a linear variety in K^n and G is a finitely generated subgroup of K^*, we show how to compute the intersection of V and G^n effectively using heights. We calculate all the estimates…
The Gaussian product inequality is an important conjecture concerning the moments of Gaussian random vectors. While all attempts to prove the Gaussian product inequality in full generality have been unsuccessful to date, numerous partial…
We formulate the necessary and sufficient conditions for the existence of a pair of maximally incompatible two-outcome measurements in a finite dimensional General Probabilistic Theory. The conditions are on the geometry of the state space,…
We show a general kinetic equality for susceptibilities (KSE) of general fluctuating quantities and for the dynamical activity of nonequilibrium systems described by Markovian master equations. As special limiting cases, KSE reproduces the…
We provide an analysis of complementarity via a suitably designed classicalmodel that leads to a set of inequalities that can be tested by means ofunsharp measurements. We show that, if the measured statistics does notfulfill the…
We give exponential upper bounds for $P(S \le k)$, in particular $P(S=0)$, where $S$ is a sum of indicator random variables that are positively associated. These bounds allow, in particular, a comparison with the independent case. We give…
Janson and Janson, Luczak and Rucinski proved several inequalities for the lower tail of the distribution of the number of events that hold, when all the events are up-sets (increasing events) of a special form - each event is the…
We study a positive-definite function associated to a measure-preserving equivalence relation on a standard probability space and use it to measure quantitatively the proximity of subequivalence relations. This is combined with a recent…