We study the expected topological properties of ˇCech and Vietoris-Rips complexes built on random points in Rd . We find higher dimensional analogues of known results for connect...
Abstract— Today, due to the vast amount of literature on largescale wireless networks, we have a fair understanding of the asymptotic behavior of such networks. However, in real ...
Given independent random points X1, . . . , Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n) > 0, we construct a random geometric graph Gn wi...