This analysis explores the distribution of integer points within translated polyhedra, revealing insights into their statistical properties.
Consider a convex body C ⊂ Rᵈ. Let X be a random point with uniform distribution in [0,1]ᵈ. Define XC as the number of lattice points in Zᵈ inside the translated body $C + X$. It is well known that E XC = vol(C). A natural question arises: What can be said about the distribution of XC in general? In this work, we study this question when C is a polyhedron with vertices at integer points.
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Aleksandr Tokmachev (2025) studied this question.
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