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• W2191001025 abstract "We establish an expression of the EC~of a $r$-regular planar set in function of some variographic quantities. The usual $mathcal{C} ^{2}$ framework is relaxed to a $mathcal{C} ^{1,1}$ regularity assumption, generalising existing local formulas for the EC. We give also general bounds on the number of connected components of a measurable set of $mathbb{R}^{2}$ in terms of local quantities. These results are then combined to yield a new expression of the mean EC~of a random regular set, depending solely on the third order marginals for arbitrarily close arguments. We derive results for level sets of some moving average processes and for the boolean model with non-connected polyrectangular grains in $mathbb{R}^{2}$. Applications to excursions of smooth bivariate random fields are derived in the companion paper cite{LacEC2}, and applied for instance to $C^{1,1}$ Gaussian fields, generalising standard results." @default.
• W2191001025 created "2016-06-24" @default.
• W2191001025 creator A5090407564 @default.
• W2191001025 date "2015-10-02" @default.
• W2191001025 modified "2023-09-27" @default.
• W2191001025 title "Bicovariograms and Euler characteristic I. Regular sets" @default.
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• W2191001025 hasPublicationYear "2015" @default.
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