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math.MG2024
Geometric embeddings of spaces of persistence diagrams with explicit distortions
Atish Mitra, Ziga Virk
Let be a positive integer. We provide an explicit geometrically motivated -Lipschitz map from the space of persistence diagrams on points (equipped with the Bottleneck d…
math.MG2019★ 8 cited
The Space of Persistence Diagrams on Points Coarsely Embeds into Hilbert Space
Atish Mitra, Žiga Virk
We prove that the space of persistence diagrams on points (with the bottleneck or a Wasserstein distance) coarsely embeds into Hilbert space by showing it is of asymptotic dime…
math.MG2013
Large scale absolute extensors
Jerzy Dydak, Atish Mitra
This paper is devoted to dualization of dimension-theoretical results from the small scale to the large scale. So far there are two approaches for such dualization: one consisting…