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تسجيل مستخدم جديدMonotonicity of functionals of random polytopes
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The convex hull $P_{n}$ of a Gaussian sample $X_{1},...,X_{n}$ in $R^{d}$ is a Gaussian polytope. We prove that the expected number of facets $E f_{d-1} (P_n)$ is monotonically increasing in $n$. Furthermore we prove this for random polytopes generated by uniformly distributed points in a $d$-dimensional ball.
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