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.PR2025
Sharp Phase Transitions for k-Fold Coverage Using Morse Theory
Yohai Reani, Omer Bobrowski
We introduce a novel approach for studying random k-coverage, using Morse theory for the k-nearest neighbor (k-NN) distance function. We prove a sharp phase transition for the numb…