Proves the strong polarization inequality and its extremal characterization in Hilbert spaces, plus asymptotic expectation, concentration, and limit shape for longest convex chains in random triangular point sets.
Valtr, The probability that n points are in convex position
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Analytic and Probabilistic Problems in Discrete Geometry
Proves the strong polarization inequality and its extremal characterization in Hilbert spaces, plus asymptotic expectation, concentration, and limit shape for longest convex chains in random triangular point sets.