The distribution of
the maximum of random fields is a relevant topics in spatial
statistics, asymptotic statistics and waves modelling.
We will present several method to give bounds,
or expansion for large levels, to this distribution, namely:
- The Rice method based on the expectation of the
numbers of local
maxima above a given level.
- The Euler Caracteristic method based on geometrical
characteristic of the excursion set above some level.
Links between the different methods are outlined and
performances and
complexity are compared.