A natural question in the study of geometric operators is that of how much information is needed to estimate the eigenvalues of an operator. For the square of the Dirac operator, such a question has at least peripheral physical import. When coupled to gauge fields, the lowest eigenvalue is related to chiral symmetry breaking. In the pure metric case, lower eigenvalue estimates may help to give ...

We consider a Poisson process η on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of η. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Itô chaos expansion. We apply these results to extend well-known variance inequal...

New classes of quadratic time-frequency representations (QTFRs), such as the affine, hyperbolic, and power classes, are interesting alternatives to the conventional shift-covariant class (Cohen's class). This paper studies new QTFR classes that retain the inner structure of Cohen's class. These classes are based on a pair of "conjugate" unitary operators and satisfy covariance and marginal prop...

We describe a method for causal inference that measures the strength of statistical dependence by the Hilbert-Schmidt norm of kernelbased conditional cross-covariance operators. We consider the increase of the dependence of two variables X and Y by conditioning on a third variable Z as a hint for Z being a common effect of X and Y . Based on this assumption, we collect “votes” for hypothetical ...

A nonparametric kernel-based method for realizing Bayes’ rule is proposed, based on kernel representations of probabilities in reproducing kernel Hilbert spaces. The prior and conditional probabilities are expressed as empirical kernel mean and covariance operators, respectively, and the kernel mean of the posterior distribution is computed in the form of a weighted sample. The kernel Bayes’ ru...

We give a mathematical framework to describe the evolution of open quantum systems subject to finitely many interactions with classical apparatuses and with each other. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently, but may also interact. This evolution, driven both by unitary operators and measurements, is coded in a mathematical...

Abstract. Calculation of Greeks by Malliavin weights has proved to be a numerically satisfactory procedure for usual Ito-diffusions. In this article we prove existence of Malliavin weights for jump diffusions under Hörmander conditions and hypotheses on the invertibility of the linkage operators. The main result – in the hypo-ellitpic case – is the invertibility of the covariance matrix, which ...

Assuming the Riemann hypothesis, we prove the weak convergence of linear statistics of the zeros of L-functions to a Gaussian field, with covariance structure corresponding to the Hnorm of the test functions. For this purpose, we obtain an approximate form of the explicit formula, relying on Selberg’s smoothed expression for ζ′/ζ and the Helffer-Sjöstrand functional calculus. Our main result is...

The subject is the applications of the use of quasi-entropy in finite dimensional spaces to many important quantities in quantum information. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the f -divergence, monotone metrics, covariance and the χ2-divergence are the most important particular cases. The extension of monotone metrics t...

Given a local homeomorphism σ : U → X where U ⊆ X is clopen and X is a compact and Hausdorff topological space, we obtain the possible transfer operators Lρ which may occur for α : C(X) → C(U) given by α(f) = f ◦ σ. We obtain examples of partial dynamical systems (XA, σA) such that the construction of the covariance algebra C (XA, σA) and the crossed product by partial endomorphism O(XA, α, L) ...