In this work, we deal with a Slater type inequality designed for symmetric convex function and collection of vectors transformed by doubly stochastic matrix. doing so, use an additional control function. the case when composition underlying is Schur-concave, such approach leads to refinement standard inequality. Special cases are also considered.

A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order O(n−1). keywords: Doubly stochastic Dirichlet distribution; Maximum-likelihood projection; Sinkhorn projection

In this paper, we obtain sharp upper and lower bounds for the smallest entries of doubly stochastic matrices of trees and characterize all extreme graphs which attain the bounds. We also present a counterexample to Merris’ conjecture on relations between the smallest entry of the doubly stochastic matrix and the algebraic connectivity of a graph in [R. Merris, Doubly stochastic graph matrices I...

In this paper a nearest doubly stochastic matrix problem is studied. This problem is to find the closest doubly stochastic matrix with the prescribed (1, 1) entry to a given matrix. According to the well-established dual theory in optimization, the dual of the underlying problem is an unconstrained differentiable but not twice differentiable convex optimization problem. A Newton-type method is ...

A positive map between Euclidean Jordan algebras is a (symmetric cone) order preserving linear map. We show that the norm of such a map is attained at the unit element, thus obtaining an analog of the operator/matrix theoretic Russo-Dye theorem. A doubly stochastic map between Euclidean Jordan algebras is a positive, unital, and trace preserving map. We relate such maps to Jordan algebra automo...

Interrelated inequalities involving doubly stochastic matrices are presented. For example, if B is an n by n doubly stochasti c matrix, x any nonnega tive vector and y = Bx, the n XIX,· •• ,x" :0:::; YIY" •• y ... Also, if A is an n by n nonnegotive matrix and D and E are positive diagonal matrices such that B = DAE is doubly s tochasti c, the n det DE ;:::: p(A) ... , where p (A) is the Perron...

Doubly stochastic measures are Borel probability measures on the unit square which push forward via the canonical projections to Lebesgue measure on each axis. The set of doubly stochastic measures is convex, so its extreme points are of particular interest. I review necessary and sufficient conditions for a set to support an extremal doubly stochastic measure, and include a proof that such a s...