  We introduce tests for the goodness of fit of point patterns via methods from
topological data analysis. More precisely, the persistent Betti numbers give
rise to a bivariate functional summary statistic for observed point patterns
that is asymptotically Gaussian in large observation windows. We analyze the
power of tests derived from this statistic on simulated point patterns and
compare its performance with global envelope tests. Finally, we apply the tests
to a point pattern from an application context in neuroscience. As the main
methodological contribution, we derive sufficient conditions for a functional
central limit theorem on bounded persistent Betti numbers of point processes
with exponential decay of correlations.
