  The paper studies the relation between critical simplices and persistence
diagrams of the \v{C}ech filtration. We show that adding a critical $k$-simplex
into the filtration corresponds either to a point in the $k$th persistence
diagram or a point in the $(k-1)$st persistence diagram. Consequently, the
number of points in persistence diagrams can be expressed in terms of the
number of critical simplices. As an application, we establish some convergence
results related to persistence diagrams of the \v{C}ech filtrations built over
binomial point processes.
