# Spectral Convergence of Empirical Graph Laplacians

#### 22.10.2015, 12:30 Uhr  –  Campus Golm, Haus 5, Raum 1.12 Forschungsseminar Diskrete Spektraltheorie

Moritz Gerlach (Potsdam)

Given a finite sequence of n samples drawn independently at random from a compact submanifold of the Euclidean space, we study the asymptotic behavior of Laplacians on the epsilon-neighborhood graph of this sample set. We show that their eigenvalues and eigenvectors converge to the eigenvalues and eigenfunctions of certain realizations of the Laplace-Beltrami operator as n tends to infinity.

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