Year: 2025
Type: preprint
Abstract: 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 number of critical points of the k-NN distance function, from which we conclude a phase transition for k-coverage. In addition, in the critical window our new framework enables us to prove a Poisson process approximation (in both location and size) for the last uncovered regions.
Source: arXiv (Cornell University)
Authors: Reani, Yohai, Bobrowski, Omer
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416619907
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