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math-ph2019
Homological Percolation and the Euler Characteristic
Omer Bobrowski, Primoz Skraba
In this paper we study the connection between the phenomenon of homological percolation (the formation of "giant" cycles in persistent homology), and the zeros of the expected Eule…
math.PR2019
Homological Connectivity in Random Čech Complexes
Omer Bobrowski
We study the homology of random Čech complexes generated by a homogeneous Poisson process. We focus on 'homological connectivity' - the stage where the random complex is dense enou…