Computational topology has recently known an important development toward
data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool
in this field...
In this paper, we study topological persistence in general
metric spaces, with a statistical approach. We show that the use of persistent
homology can be naturally considered in general statistical frameworks and
persistence diagrams can be used as statistics with interesting convergence
properties. Some numerical experiments are performed in various contexts to
illustrate our results.