Multiple hypothesis testing with persistent homology

In this paper we propose a computationally efficient multiple hypothesis testing procedure for persistent homology. The computational efficiency of our is based on the observation that one can empirically simulate null distribution universal across many applications involving persistence Our suggests efficiently small number summaries collected data and use in same way p-value tables were used classical statistics. To illustrate utility provide procedures rejecting acyclicity with both control Family-Wise Error Rate (FWER) False Discovery (FDR). We will argue empirical very general conditional few simulations limit theorems homology point processes.