On the perturbation of Markov chains with nearly transient states.
On the volume of the double stochastic matrices.
On the volume of the polytope of doubly stochastic matrices.
Perfect sampling from the limit of deterministic products of stochastic matrices.
Products of stochastic matrices and applications.
Random matrices, magic squares and matching polynomials.
Random walk centrality and a partition of Kemeny's constant
We consider an accessibility index for the states of a discrete-time, ergodic, homogeneous Markov chain on a finite state space; this index is naturally associated with the random walk centrality introduced by Noh and Reiger (2004) for a random walk on a connected graph. We observe that the vector of accessibility indices provides a partition of Kemeny's constant for the Markov chain. We provide three characterizations of this accessibility index: one in terms of the first return time to the state...
Remarks on doubly substochastic rectangular matrices
Some subpolytopes of the Birkhoff polytope.
Star matrices: properties and conjectures.
Subdominant eigenvalues for stochastic matrices with given column sums.
Sur l'orthogonalité de deux lois de probabilités correspondant à deux processus de Markov
Symmetric stochastic matrices with given row sums.
Characterizations of extreme infinite symmetric stochastic matrices with respect to arbitrary non-negative vector r are given.
Technical comment. A problem on Markov chains
A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.
Technical comment. A problem on Markov chains
A problem (arisen from applications to networks) is posed about the principal minors of the matrix of transition probabilities of a Markov chain.
The Dittert's function on a set of nonnegative matrices.
The structure of linear operators strongly preserving majorizations of matrices.
The structure of linear preservers of left matrix majorization on .
The theory and applications of complex matrix scalings
We generalize the theory of positive diagonal scalings of real positive definite matrices to complex diagonal scalings of complex positive definite matrices. A matrix A is a diagonal scaling of a positive definite matrix M if there exists an invertible complex diagonal matrix D such that A = D*MD and where every row and every column of A sums to one. We look at some of the key properties of complex diagonal scalings and we conjecture that every n by n positive definite matrix has at most 2n−1 scalings...
Trace inequalities with applications to orthogonal regression and matrix nearness problems.