相关论文: On the thin-shell conjecture for the Schatten clas…

We prove criteria for a {\it 'magnetic' Weyl operator} to be in a Schatten-von Neuman class by extending a method developed by H. Cordes, T. Kato and G. Arsu.

We introduce and study a new class of operators that we call disjoint weak Banach-Saks operators. We establish some characterizations of this class of operators by different types of convergence (norm convergence, unbounded order…

Heisenberg and Schr{\"o}dinger uncertainty principles give lower bounds for the product of variances $Var_{\rho}(A)\cdot Var_{\rho}(B)$, in a state $\rho$, if the observables $A,B$ are not compatible, namely if the commutator $[A,B]$ is not…

In this paper, we introduce and study the class of {\it enriched strictly pseudocontractive mappings} in Hilbert spaces and extend the corresponding convergence theorem (Theorem 12) in [Browder, F. E., Petryshyn, W. V., {\it Construction of…

We discuss restrictions on operators in the soft-collinear effective theory (SCET) which follow from the ambiguity in the decomposition of collinear momenta and the freedom in the choice of light-like basis vectors $n$ and $\bar n$.…

Order statistics theory is applied in this paper to probabilistic robust control theory to compute the minimum sample size needed to come up with a reliable estimate of an uncertain quantity under continuity assumption of the related…

Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular weak tail domination implies strong tail domination. In…

Let X be a smooth variety over a number field k embedded as a degree d subvariety of $\mathbb{P}^n$ and suppose that X is a counterexample to the Hasse principle explained by the Brauer-Manin obstruction. We consider the question of whether…

We define 2-indexed $(q,p)$-Schatten quasi-norms for any $q,p > 0$ on operators on a tensor product of Hilbert spaces, naturally extending the norms defined by Pisier's theory of operator-valued Schatten spaces. We establish several…

We prove an invariant Harnack's inequality for operators in non-divergence form structured on Heisenberg vector fields when the coefficient matrix is uniformly positive definite, continuous, and symplectic. The method consists in…

We show that under some assumptions on the monodromy group some combinations of higher Chern classes of flat vector bundles are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles…

Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently…

In \cite{PRA} and \cite{SSM} the orthonormal Strichartz estimates for the Schr\"odinger equation associated with the Dunkl Laplacian and the Dunkl-Hermite operator are obtained. In this article, we prove a necessary condition on the…

In this paper, we prove a novel trace inequality involving two operators. As applications, we sharpen the one-shot achievability bound on the relative entropy error in a wealth of quantum covering-type problems, such as soft covering,…

Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…

The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $\theta$-weak…

Suppose we have data generated according to a multivariate normal distribution with a fixed unknown mean vector that is sparse in the sense of being nearly black. Optimality of Bayes estimates and posterior concentration properties in terms…

We investigate the interplay among three key properties of bounded linear operators between Banach spaces: the Bhatia-\v{S}emrl property, strong subdifferentiability and the condition that the essential norm is strictly less than the…

We consider the problem of inference after model selection under weak assumptions in the time series setting. Even when the data are not independent, we show that sample splitting remains asymptotically valid as long as the process…

It is conjectured that within the class group of any number field, for every integer $\ell \geq 1$, the $\ell$-torsion subgroup is very small (in an appropriate sense, relative to the discriminant of the field). In nearly all settings, the…