4 papers · 1 filter
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…
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…
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…
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…