相关论文: An Inequality for the Correlation of Two Functions…
We prove a set of inequalities that interpolate the Cauchy-Schwarz inequality and the triangle inequality. Every nondecreasing, convex function with a concave derivative induces such an inequality. They hold in any metric space that…
We prove an inequality for unitarily invariant norms that interpolates between the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality.
A generalized Cauchy-Schwarz inequality is derived and applied to uncertainty relation in quantum mechanics. We see a modification in the uncertainty relation and minimum uncertainty wave packet.
We prove a general inequality for more than two sequences mirroring that of the discrete two-sequence Cauchy-Schwarz.
We show how the Schroedinger Uncertainty Relation for a pair of observables can be deduced using the Cauchy-Schwarz inequality plus successive applications of the commutation relation involving the two observables. Our derivation differs…
In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and solve some special cases for a spherical correlation…
The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive…
Motivated by some applications to calculating order of poles of certain (local or global) $L$-functions, the author considers a Cauchy-Schwarz type inequality for representations of SU(2).
In this paper, we compare two variances of maxima of $N$ standard Gaussian random variables. One is a sequence of $N$ i.i.d. standard Gaussians, and the other one is $N$ standard Gaussians with covariances $\sigma_{1,2}=\rho \in(0,1)$ and…
We consider the Sobolev norms of the pointwise product of two functions, and estimate from above and below the constants appearing in two related inequalities.
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
The Cauchy-Schwarz (CS) inequality -- one of the most widely used and important inequalities in mathematics -- can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities. Quantum…
A positive correlation inequality is established for circular-invariant plurisubharmonic functions, with respect to complex Gaussian measures. The main ingredients of the proofs are the Ornstein-Uhlenbeck semigroup, and another natural…
For convex univalent functions we give instances where the sharp bound for various coefficient functionals are identical to those for the corresponding bound for the inverse function. We give instances where the sharp bounds differ and also…
We derive strong variance-based uncertainty relations for arbitrary two and more unitary operators by re-examining the mathematical foundation of the uncertainty relation. This is achieved by strengthening the celebrated Cauchy-Schwarz…
In this paper, we establish a new inequality tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We…
We prove two conjectures on correlation inequalities for functions that are linear combinations of unimodal Boolean monotone nondecreasing functions
This note demonstrates that it is possible to bound the expectation of an arbitrary norm of a random matrix drawn from the Stiefel manifold in terms of the expected norm of a standard Gaussian matrix with the same dimensions. A related…
The Riesz-Sobolev inequality relates the convolution of nonnegative functions on Euclidean space to the convolution of their symmetric nonincreasing rearrangements. We show that for dimension one, for indicator functions of sets, if the…
Destructive interference-based photon-phonon antibunching can lead to violations of classical inequalities in optomechanical cavity systems. In this paper, we explore the violation of the classical Cauchy-Schwarz inequality by examining…