10 citations · 11 across the 4 of their papers we have counts for
4 papers · 1 filter
Homological Percolation: The Formation of Giant k-Cycles
Omer Bobrowski, Primoz Skraba
In this paper we introduce and study a higher-dimensional analogue of the giant component in continuum percolation. Using the language of algebraic topology, we define the notion o…
On the Spectrum of Dense Random Geometric Graphs
Kartick Adhikari, Robert J. Adler, Omer Bobrowski +1
In this paper we study the spectrum of the random geometric graph , in a regime where the graph is dense and highly connected. In the \erdren random graph it is we…
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…
Crackle: The Persistent Homology of Noise
Robert J. Adler, Omer Bobrowski, Shmuel Weinberger
We study the homology of simplicial complexes built via deterministic rules from a random set of vertices. In particular, we show that, depending on the randomness that generates t…