A course in Gaussian processes. At first we shall study basic facts about Gaussian processes - isoperimetric inequality and concentration, comparison inequalities, boundedness and continuity of Gaussian processes, Gaussian series of functions, etc. Later we specialize to smooth Gaussian processes and their nodal sets , in particular expected length and number of nodal sets, persistence probability and other such results from recent papers of many authors.
Suggested books and references:
Robert Adler and Jonathan Taylor, Gaussian Random Fields
,Springer, New York, 2007.
Svante Janson, Gaussian Hilbert Spaces
,Cambridge University Press, Cambridge, 1997.
A. I. Bogachev, Gaussian Measures
,American Mathematical Society, Providence, RI, 1998.
Michel Ledoux and Michel Talagrand, Probability in Banach spaces. Isoperimetry and processes
,Springer-Verlag, Berlin, 2011.
Michel Ledoux, Isoperimetry and Gaussian analysis
,St. Flour lecture notes-1994.