Permanental Vectors

A permanental vector is a generalization of a vector with components that are squares of the components of a Gaussian vector, in the sense that the matrix that appears in the Laplace transform of the vector of Gaussian squares is not required to be either symmetric or positive definite. In addition the power of the determinant in the Laplace transform of the vector of Gaussian squares, which is -1/2, is allowed to be any number less than zero. It was not at all clear what vectors are permanental vectors. In this paper we characterize all permanental vectors in $R^{3}_{+}$ and give applications to permanental vectors in $R^{n}_{+}$ and to the study of permanental processes

On Critical Points for Gaussian Vectors with Infinitely Divisible Squares

Investigates the size of the perturbation to the zero mean three dimensional Gaussian vector with infinitely divisible squares so that the infinite divisibility is retained

Fixation for coarsening dynamics in 2D slabs

For the zero temperature limit of Ising Glauber Dynamics on 2D slabs the existence or nonexistence of vertices that do not fixate is determined as a function of slab thickness.Comment: 16 pages, 9 figure

Permanental processes

This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian process is replaced by a function that is not necessarily symmetric nor positive definite, but that nevertheless determines a stochastic process. This is a new avenue of research with very many open problems.Comment: 31 page