Showing math.MGShow all
3 papers · 1 filter
math.MG2025
On the signature of squared distance matrices of metric measure spaces
Alexey Kroshnin, Tianyu Ma, Eugene Stepanov
We consider the numbers of positive and negative eigenvalues of matrices of squared distances between randomly sampled i.i.d. points in a given metric measure space. These numbers…
math.MG2024
On the total surface area of potato packings
Matteo Novaga, Emanuele Paolini, Eugene Stepanov
We prove that if we fill without gaps a bag with infinitely many potatoes, in such a way that they touch each other in few points, then the total surface area of the potatoes must…
math.MG2024
On eigenvalues and eigenfunctions of the operators defining multidimensional scaling on some symmetric spaces
Tianyu Ma, Eugene Stepanov
We study asymptotics of the eigenvalues and eigenfunctions of the operators used for constructing multidimensional scaling (MDS) on compact connected Riemannian manifolds, in parti…