  We give a criterion which characterizes a real multi-variate Laurent
polynomial with full-dimensional smooth Newton polytope to have the property
that all sufficiently large powers of the polynomial have fully positive
coefficients. Here a Laurent polynomial is said to have fully positive
coefficients if the coefficients of its monomial terms indexed by the lattice
points of its Newton polytope are all positive. Our result generalizes an
earlier result of the authors, which corresponds to the special case when the
Newton polytope of the Laurent polynomial is a translate of a standard simplex.
The result also generalizes a result of De Angelis, which corresponds to the
special case of univariate polynomials. As an application, we also give a
characterization of certain polynomial spectral radius functions of the
defining matrix functions of Markov chains.
