A real or complex n × n matrix is generalized doubly stochastic if all of its row sums and column sums equal one. Denote by V the linear space spanned by such matrices. We study the reducibility of V under the group Γ of linear operators of the form A 7→ PAQ, where P and Q are n×n permutation matrices. Using this result, we show that every linear operator φ : V → V mapping the set of generalize...

We investigate the properties of uniform doubly stochastic random matrices, that is non-negative matrices conditioned to have their rows and columns sum to 1. The rescaled marginal distributions are shown to converge to exponential distributions and indeed even large sub-matrices of side-length o(n) behave like independent exponentials. We determine the limiting empirical distribution of the si...

let a and b be n × m matrices. the matrix b is said to be g-row majorized (respectively g-column majorized) by a, if every row (respectively column) of b, is g-majorized by the corresponding row (respectively column) of a. in this paper all kinds of g-majorization are studied on mn,m, and the possible structure of their linear preservers will be found. also all linear operators t : mn,m ---> mn...

A sharp lower bound for the smallest entries, among those corresponding to edges, of doubly stochastic matrices of trees is obtained, and the trees that attain this bound are characterized. This result is used to provide a negative answer to Merris’ question in [R. Merris, Doubly stochastic graph matrices II, Linear Multilin. Algebra 45 (1998) 275–285]. © 2005 Elsevier Inc. All rights reserved....

In Ehrhart theory, the h∗-vector of a rational polytope often provides insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic matrices, has a unimodal h∗-vector, but when even small modifications are made to the polytope, the same property can be very difficult to prove. In this paper, w...

Let Tn be the compact convex set of tridiagonal doubly stochastic matrices. These arise naturally in probability problems as birth and death chains with a uniform stationary distribution. We study ‘typical’ matrices T ∈ Tn chosen uniformly at random in the set Tn. A simple algorithm is presented to allow direct sampling from the uniform distribution on Tn. Using this algorithm, the elements abo...