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Lipschitz Functions Have Lp-Stable Persistence
David Cohen-Steiner, Herbert Edelsbrunner, John Harer, Yuriy Mileyko
We prove two stability results for Lipschitz functions on triangulable, compact metric spaces and consider applications of both to problems in systems biology. Given two functions, the first result is formulated in terms of the Wasserstein distance between their persistence diagrams and the second in terms of their total persistence.