 
Summary: arXiv:0910.0763v1[math.PR]5Oct2009
Some applications of Rice formulas to waves
JeanMarc Aza¨is
Jos´e R. Le´on
Mario Wschebor
October 5, 2009
Abstract
We use Rice's formulas in order to compute the moments of some
level functionals which are linked to problems in oceanography and op
tics. For instance, we consider the number of specular points in one or
two dimensions, the number of twinkles, the distribution of normal angle
of level curves and the number or the length of dislocations in random
wavefronts. We compute expectations and in some cases, also second mo
ments of such functionals. Moments of order greater than one are more
involved, but one needs them whenever one wants to perform statistical
inference on some parameters in the model or to test the model itself.
In some cases we are able to use these computations to obtain a Central
Limit Theorem.
AMS Subject Classification: Primary 60G15; Secondary 60G60 78A10 78A97
86A05
