Čech complex 1persistent homology 1random point processes 1triangulable spaces 1Vietoris-Rips complex 1
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math.PR2026
Universal topological statistics on triangulated singular spaces
Uzu Lim, Omer Bobrowski, Primoz Skraba
The paper proves that the expected persistent homology of random point clouds on a wide class of triangulable spaces converges to a universal limit that does not depend on the spec…
math.PR2026
Sharp Phase Transition for the Formation of Infinite Tubes
Shu Kanazawa, Omer Bobrowski, Primoz Skraba
Classical bond percolation theory studies the conditions for a given point in a random graph to be connected to infinity, or "escape" to infinity, via a sequence of random edges. I…
math.PR2024
Universality in Random Persistent Homology and Scale-Invariant Functionals
Omer Bobrowski, Primoz Skraba
In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point processes. Specifically, we…