Related papers: Majorization: Here, There and Everywhere
We introduce a definition of multivariate majorization that is new to the economics literature. Our majorization technique allows us to generalize Mussa and Rosen's (1978) "ironing" to a broad class of multivariate principal-agents…
Considering the weighted concept of majorization, Sherman obtained generalization of majorization inequality for convex functions known as Sherman's inequality. We extend Sherman's result to the class of n-strongly convex functions using…
We consider positive, integral-preserving linear operators acting on $L^1$ space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of…
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
Expander graphs have been, during the last five decades, the subject of a most fruitful interaction between pure mathematics and computer science, with influence and applications going both ways (cf. [Lub94], [HLW06], [Lub12] and the…
There has been much discussion in the literature about rival measures of classical polarization in three dimensions. We gather and compare the various proposed measures of polarization, creating a geometric representation of the…
The main result of this paper is the extension of the Schur-Horn Theorem to infinite sequences: For two nonincreasing nonsummable sequences x and y that converge to 0, there exists a compact operator A with eigenvalue list y and diagonal…
Although an input distribution may not majorize a target distribution, it may majorize a distribution which is close to the target. Here we introduce a notion of approximate majorization. For any distribution, and given a distance $\delta$,…
In this paper, we introduce novel characterizations of the classical concept of majorization in terms of upper triangular (resp., lower triangular) row-stochastic matrices, and in terms of sequences of linear transforms on vectors. We used…
The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on $\mathbb{R}^n$. Rearrangements are maps that are monotonic (up to sets of measure zero) and…
Allocating resources to individuals in a fair manner has been a topic of interest since the ancient times, with most of the early rigorous mathematical work on the problem focusing on infinitely divisible resources. Recently, there has been…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
Schur multipliers were introduced by Schur in the early 20th century and have since then found a considerable number of applications in Analysis and enjoyed an intensive development. Apart from the beauty of the subject in itself, sources…
We consider recent work linking majorization and trumping, two partial orders that have proven useful with respect to the entanglement transformation problem in quantum information, with general Dirichlet polynomials, Mellin transforms, and…
One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into the probability vectors of the other. This is called matrix…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
Uncertainty is prevalent in engineering design, data-driven problems, and decision making broadly. Due to inherent risk-averseness and ambiguity about assumptions, it is common to address uncertainty by formulating and solving conservative…
It is a matter of debate whether a shrinking proportion of scholarly literature is getting most of the references over time. It is also less well understood how a narrowing literature usage would affect the circulation of ideas in the…
The Hardy-Littlewood-P\'{o}lya inequality of majorization is extended to the framework of ordered Banach spaces. Several applications illustrating our main results are also included.