# Some applications of Rice formulas to waves - Mathematics > Probability

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Abstract: We use Rice-s formulas in order to compute the moments of some levelfunctionals which are linked to problems in oceanography and optics. Forinstance, we consider the number of specular points in one or two dimensions,the number of twinkles, the distribution of normal angle of level curves andthe number or the length of dislocations in random wavefronts. We computeexpectations and in some cases, also second moments of such functionals.Moments of order greater than one are more involved, but one needs themwhenever one wants to perform statistical inference on some parameters in themodel or to test the model itself. In some case we are able to use thesecomputations to obtain a Central Limit Theorem.

Author: ** Jean-Marc Azaïs University of Toulouse, José R. León Universidad Central de Venezuela, Mario Wschebor Universidad de la Repúb**

Source: https://arxiv.org/