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Found Comput Math DOI 10.1007/s10208-010-9067-z

Summary: Found Comput Math
DOI 10.1007/s10208-010-9067-z
Jean-Marc Azaïs and Mario Wschebor: Level Sets
and Extrema of Random Processes and Fields
Wiley, 2009. ISBN: 978-0-470-40933-6. 393 pages. £73.50
Didier Dacunha-Castelle
Received: 8 February 2010 / Revised: 18 February 2010 / Accepted: 18 February 2010
© SFoCM 2010
The book of Azaïs and Wschebor is dedicated mainly, as the title says, to level sets
and extrema of random fields and processes, but it contains also many other important
results, for instance related to the use of random matrices in the study of the existence
of real solutions for large systems of linear or polynomial equations, to statistical
tests, and to genetics and oceanography.
It is a very original book, distinguished by its topic and its ability to make use
of intuitive basic techniques, such as the Rice formula for instance. So we can say
already that it is one of the most important books in probability theory published in
the last twenty years. The approach to processes and fields described in this book is
from my point of view just at the beginning of its applications and consequences even
if the Rice formulas have been known for a long time. I will try to say why later.


Source: Azais, Jean-Marc -Institut de Mathématiques de Toulouse, Université Paul Sabatier


Collections: Mathematics