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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.MG2025
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…