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math.PR2026
A Universal Law of Large Numbers for Extreme Cycles in Random Čech Complexes
Omer Bobrowski, Primoz Skraba
We study the maximal multiplicative persistence of -cycles in random Čech complexes. Let be a probability density function, let be a Poisso…
math.PR2026
Universal topological statistics on triangulated singular spaces
Uzu Lim, Omer Bobrowski, Primoz Skraba
We prove a universality theorem for random persistent homology over a class of triangulable spaces. More precisely, let be a compact -triangulable spa…
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…