Related papers: Extending a characterization of majorization to in…
We apply concepts of majorization theory to derive new insights in the field of extremal dependence structures. In particular, we consider the Rearrangement Algorithm by Puccetti and Rueschendorf, where majorization arguments yield a…
Fundamental domains are found for functions defined by general Dirichlet series and using basic properties of conformal mappings the Great Riemann Hypothesis is studied.
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple…
We present some exact results about universal quantities derived from the local density matrix, for a free massive Dirac field in two dimensions. We first find the trace of powers of the density matrix in a novel fashion, which involves the…
We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general…
In one-dimensional Diophantine approximation, the Diophantine properties of a real number are characterized by its partial quotients, especially the growth of its large partial quotients. Notably, Kleinbock and Wadleigh [Proc. Amer. Math.…
Let $k \geq 2$ be an integer. We prove that factorization of integers into $k$ parts follows the Dirichlet distribution $\text{Dir}\left(\frac{1}{k},\ldots,\frac{1}{k}\right)$ by multidimensional contour integration, thereby generalizing…
This paper surveys recent developments in the sampling discretization of integral and uniform norms for functions in general finite-dimensional spaces. These results generalize the classical Marcinkiewicz-Zygmund inequalities for…
We establish sharp upper bounds for shifted moments of quadratic Dirichlet $L$-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
What does it mean for one quantum process to be more disordered than another? Here we provide a precise answer to this question in terms of a quantum-mechanical generalization of majorization. The framework admits a complete description in…
We propose a monotone, and consistent numerical scheme for the approximation of the Dirichlet problem for the normalized Infinity Laplacian, which could be related to the family of so--called two--scale methods. We show that this method is…
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
We initiate the study of the norm-squared of the momentum map as a rigorous tool in infinite dimensions. In particular, we calculate the Hessian at a critical point, show that it is positive semi-definite along the complexified orbit, and…
We argue that a complete characterisation of quantum correlations in bipartite systems of many dimensions may require a quantity which, even for pure states, does not reduce to a single number. Subsequently, we introduce multi-dimensional…
Majorization inequalities for symmetric polynomials have interested mathematicians for centuries, from the AM-GM inequality for two variables going back at least to Euclid, through classical results of Newton, Muirhead and Gantmacher, to…
The theory of majorization and its variants, including thermomajorization, have been found to play a central role in the formulation of many physical resource theories, ranging from entanglement theory to quantum thermodynamics. Here we…
We show continuity in generalized weighted Morrey spaces of sub-linear integral operators generated by some classical integral operators and commutators. The obtained estimates are used to study global regularity of the solution of the…