Optimal pointwise lower bounds for even log-concave densities

Prelegent(ci)

Daniel Murawski

Afiliacja

University of Warsaw

Język referatu

angielski

Termin

22 stycznia 2026 12:15

Pokój

p. 3160

Tytuł w języku polskim

Optimal pointwise lower bounds for even log-concave densities

Seminarium

Seminarium Zakładu Rachunku Prawdopodobieństwa

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We show that among all symmetric real log-concave random variables X with variance 1 and any t_0 in range [0, √3] the quantity f_X(t_0) is minimized by a uniform, Laplace or truncated Laplace distribution. We show that for t_0 ≥ 1/√2 the minimum is attained by Laplace distribution and for t_0 ≤ 1/2 it is attained by uniform distribution. We also show that the constant 1/√2 cannot be improved and that there exist t_0 such that the minimizer is neither Laplace or uniform. This gives optimal dimension-free lower bounds for measures of non-central slices of isotropic convex bodies.

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