6 papers
Hermite-Fisher bounds and stability for min-entropy power inequalities
Silouanos Brazitikos, Martin Rapaport, Tomasz Tkocz
We derive explicit lower bounds for relative Fisher information by combining a variational principle with suitably orthogonalized Hermite-polynomial test functions. The resulting c…
Moments of sums of exponentials, beyond CHS
Silouanos Brazitikos, Colin Tang, Tomasz Tkocz
We establish a sharp lower bound on the -norm of sums of independent exponential random variables with fixed variance, for , thus extending Hunter's positivity theor…
Negative Moments of Steinhaus Sums
Martin Rapaport, Tomasz Tkocz, Isabella Wu
We prove a sharp upper bound on negative moments of sums of independent Steinhaus random variables (that is uniform on circles in the plane). Together with the series of earlier wo…
Khinchin inequalities for uniforms on spheres with a deficit
Jacek Jakimiuk, Colin Tang, Tomasz Tkocz
We sharpen the moment comparison inequalities with sharp constants for sums of random vectors uniform on Euclidean spheres, providing a deficit term (optimal in high dimensions).
Stability of simplex slicing
Serhii Myroshnychenko, Colin Tang, Kateryna Tatarko +1
We establish dimension-free stability of Webb's sharp simplex slicing (1996). Incidentally, we investigate Lipschitzness of volume of hyperplane central sections of arbitrary (not…
Convexity properties of sections of 1-symmetric bodies and Rademacher sums
Joseph Kalarickal, David Rotunno, Salil Singh +1
We establish a monotonicity-type property of volume of central hyperplane sections of the 1-symmetric convex bodies, with applications to chessboard cutting. We parallel this for p…