Characterization of Polynomials Whose Large Powers have Fully Positive Coefficients

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