Betti numbers, Euler characteristic and their sum for excursion sets are expressed in terms of Binomial coefficients of a topological basis, predicting Gaussian statistics except at high thresholds.
Such exam- ples arise when some physical process erases small and/or lager scale fluctuations
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On the statistical nature of Betti numbers and Euler characteristic of smooth random fields
Betti numbers, Euler characteristic and their sum for excursion sets are expressed in terms of Binomial coefficients of a topological basis, predicting Gaussian statistics except at high thresholds.