4 citations · 6 across the 11 of their papers we have counts for
5 papers · 1 filter
Limit theorems for the volumes of small codimensional random sections of -balls
Radosław Adamczak, Peter Pivovarov, Paul Simanjuntak
We establish Central Limit Theorems for the volumes of intersections of (the unit ball of ) with uniform random subspaces of codimension for fixed and $…
Randomized Urysohn-type inequalities
Thomas Hack, Peter Pivovarov
As a natural analog of Urysohn's inequality in Euclidean space, Gao, Hug, and Schneider showed in 2003 that in spherical or hyperbolic space, the total measure of totally geodesic…
On sharp bounds for marginal densities of product measures
Galyna Livshyts, Grigoris Paouris, Peter Pivovarov
We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if is a probability density on of the form $f(x)=\prod_{i=1…
Bounding marginal densities via affine isoperimetry
Susanna Dann, Grigoris Paouris, Peter Pivovarov
Let be a probability measure on with a bounded density . We prove that the marginals of on most subspaces are well-bounded. For product measures, studied…
A central limit theorem for projections of the cube
Grigoris Paouris, Peter Pivovarov, Joel Zinn
We prove a central limit theorem for the volume of projections of the N-cube onto a random subspace of dimension n, when n is fixed and N tends to infinity. Randomness in this case…