Topological data analysis of continuum percolation with disks

We study continuum percolation with disks, a variant of continuum percolation in two-dimensional Euclidean space, by applying tools from topological data analysis. We interpret each realization of continuum percolation with disks as a topological subspace of $[0,1]^2$ and investigate its topological features across many realizations. We apply persistent homology to investigate topological changes as we vary the number and radius of disks. We observe evidence that the longest persisting invariant is born at or near the percolation transition.