Conditional S-matrices

Mean matrices and conditional negativity

Conditional Autoregressions with Doubly Stochastic Weight Matrices

A conditional spatial autoregression (CAR) specifies dependence via a weight matrix. Employing a doubly stochastic weight matrix allows users to interpret the CAR prediction rule as a semiparametric prediction rule and as BLUP with smoothing in addition to other benefits. We examine standard and doubly stochastic weight matrices in the context of an illustrative data set to demonstrate feasibil...

Positivity and Conditional Positivity of Loewner Matrices

We give elementary proofs of the fact that the Loewner matrices [ f(pi)−f(pj) pi−pj ] corresponding to the function f(t) = t on (0,∞) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0,∞) the Loewner matrices corresponding to an operator convex function on...

S-constrained random matrices

Let S be a set of d-dimensional row vectors with entries in a q-ary alphabet. A matrix M with entries in the same q-ary alphabet is S-constrained if every set of d columns ofM contains as a submatrix a copy of the vectors in S, up to permutation. For a given set S of d-dimensional vectors, we compute the asymptotic probability for a random matrix M to be S-constrained, as the numbers of rows an...

Deriving boundary S matrices

We show how to derive exact boundary S matrices for integrable quantum field theories in 1+1 dimensions using lattice regularization. We do this calculation explicitly for the sine-Gordon model with fixed boundary conditions using the Bethe ansatz for an XXZtype spin chain in a boundary magnetic field. Our results agree with recent conjectures of Ghoshal and Zamolodchikov, and indicate that the...