Manjunath Krishnapur

Department of Mathematics, Indian Institute of Science, Bangalore 560 012

Gaussian processes (Spring 2014)

Tue, Thu 2:00-3:30, LH-5
(new wing, second floor, deparment of mathematics)

Description: 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.

Grading: Those who credit the course can get grade A by solving many exercise problems and making a presentation, grade B by failing to do some of these and grade S by doing something more.

Texts and other resources: In no particular order (I may sample material from many places) -
  1. Robert Adler and Jonathan Taylor Gaussian Random Fields, Springer, New York, 2007.
  2. Svante Janson Gaussian Hilbert Spaces, Cambridge University Press, Cambridge, 1997
  3. V. I. Bogachev Gaussian Measures, American Mathematical Society, Providence, RI, 1998.
  4. Michel Ledoux and Michel Talagrand Probability in Banach spaces. Isoperimetry and processes, Springer-Verlag, Berlin, 2011.
  5. Boris Tsirelson Lecture notes from a course
  6. Michel Ledoux Isoperimetry and Gaussian analysis, St. Flour lecture notes-1994.

Notes for specific topics: