A. Tokmachev

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20242026

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math.PR2026

Inequalities for convex functions of random points inside and on the boundary of convex bodies

A. S. Tokmachev

Let $K$ be a convex body in $R^{d}$ , and let $I$ and $B$ be random points uniformly distributed inside $K$ and on its boundary, respectively. We prove that if $d = 2$ and $\ma…

math.PR2025

On integer points inside a randomly shifted polyhedron

Aleksandr Tokmachev

Consider a convex body $C \subset R^{d}$ . Let $X$ be a random point with uniform distribution in $[0, 1]^{d}$ . Define $X_{C}$ as the number of lattice points in $Z^{d}$ in…

math.PR2024

Lattice points inside a random shifted integer polygon

Aleksandr Tokmachev

Consider a convex body $C \subset R^{d}$ . Let $X$ be a random point with uniform distribution in $[0, 1]^{d}$ . Consider the value $X_{C}$ equal to the number of lattice points $\…