5 papers
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).
From simplex slicing to sharp reverse Hölder inequalities
James Melbourne, Michael Roysdon, Colin Tang +1
Simplex slicing (Webb, 1996) is a sharp upper bound on the volume of central hyperplane sections of the regular simplex. We extend this to sharp bounds in the probabilistic framewo…
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…
Adaptive Matrix Sparsification and Applications to Empirical Risk Minimization
Yang P. Liu, Richard Peng, Colin Tang +2
Consider the empirical risk minimization (ERM) problem, which is stated as follows. Let be compact convex sets with for $i \in [m…
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…