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math.ST2021
A functional central limit theorem for the empirical Ripley's K-function
Christophe A. N. Biscio, Anne Marie Svane
We establish a functional central limit theorem for Ripley's K-function for two classes of point processes. One is the class of point processes having exponential decay of correlat…
math.ST2019
Testing goodness of fit for point processes via topological data analysis
Christophe Ange Napoléon Biscio, Nicolas Chenavier, Christian Hirsch +1
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 funct…