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Persistent homology and random models of the Gaussian primes. (English) Zbl 1439.11239
Summary: I. Vardi introduced a probabilistic model for the distribution of Gaussian primes in [Exp. Math. 7, No. 3, 275–289 (1998; Zbl 0926.11065)]. We use persistent homology to test how well Vardi’s model and a symmetrized variant of Vardi’s model capture the geometry of the Gaussian primes. An analysis of the persistent first homology of point clouds produced by these models provides statistical evidence that the models miss some fundamental geometric features of the Gaussian primes.
11N05 Distribution of primes
55N35 Other homology theories in algebraic topology
55N31 Persistent homology and applications, topological data analysis
Dionysus; PHAT
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