Limits of polyhedral multinomial distributions

03/27/2023

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by   Aniket Shah, et al.

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We consider limits of certain measures supported on lattice points in lattice polyhedra defined as the intersection of half-spaces {m∈ℝ^n|⟨ v_i,x⟩+a_i ≥ 0}, where ∑_i v_i = 0. The measures are densities associated to lattice random variables obtained by restriction of multinomial random variables. We find the limiting Gaussian distributions explicitly.