No abstract

Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varietes we prove convergence results for sequences of distribution functions ϕ n = |s N |/ s N L 2 for sections s N ∈ Γ(X, L N ) approaching a semiclassical ray. Here X is a normal compact toric variety and L is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch [STZ].