Gaussian measures and Gaussian processes

2004/2005, sem. 2

Prof. Boris Tsirelson (School of Mathematical Sciences).
Time and place
Thursday 16-19 Dan David 207.
Be acquainted with such things as the Hilbert space L2 of square integrable functions on a measure space. Everything else will be explained from scratch. However, some maturity in analysis is needed. (Maturity in probability is not needed.)

Note: no classes on May 19 (because of the IMU conference) and May 26 (because of the students day).
Instead we plan classes on May 23 (16-19, Ornstein 102) and May 24 (16-19, Shenkar 222).

A quote:

"Gaussian random variables and processes always played a central role in the probability theory and statistics. The modern theory of Gaussian measures combines methods from probability theory, analysis, geometry and topology and is closely connected with diverse applications in functional analysis, statistical physics, quantum field theory, financial mathematics and other areas."

R. Latala, On some inequalities for Gaussian measures. Proceedings of the International Congress of Mathematicians (2002), 813-822. arXiv:math.PR/0304343.

Some literature

Lecture notes

  1. Basic notions.
    PDF or Postscript.
  2. Concentration of Gaussian measure.
    PDF or Postscript.
  3. Gaussian random matrices.
    PDF or Postscript.
  4. Frozen disorder in physical systems.
    PDF or Postscript.