Abstract:
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The expected Euler Characteristic (EC) of the excursion set for random fields is used to approximate the distribution of the maximum of the field. This expected value is derived for many random fields, mainly, using a generalized version of Rice's approach for one-dimensional fields. In this work, by considering the EC of the excursion set at the threshold level u, as a point process with the parameter u, the expected EC is derived for a centralized, unit variance Gaussian field. The suggested method can be used for other Gaussian related random fields.
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