Abstract
Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties convergence results for sequences of distribution functions ϕ_n=|s_N| / |s_N|_{L^2} for sections s_N\in Γ(X,L^N) approaching a semiclassical ray are proved. 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.
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