Let M be a bounded domain of R^d with smooth boundary. We relate the Cheeger constant of M and the Cheeger constant of a neighborhood graph defined on a random sample from M. By restricting the minimization defining the latter over a particular class of subsets, we obtain consistency (after normalization) as the sample size increases, and show that any minimizing sequence of subsets has a subsequence converging to a Cheeger set of M.

Joint work with Bruno Pelletier and Pierre Pudlo.