## TAU:0366-4765 |
## Gaussian measures | ## 2010/2011, sem. 1 |

- Lecturer
- Prof. Boris Tsirelson (School of Mathematical Sciences).
- Time and place
- Tuesday 10-13, Schreiber 209.
- Prerequisites
- Be acquainted with such things as the Hilbert space
*L*_{2}of square integrable functions on a measure space, and the normal distribution. Everything else will be explained from scratch. However, some maturity in analysis is needed. (Maturity in probability is not needed.) - Grading policy
- Written homework and oral exam.

"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.

- Random real zeroes: no derivatives.
- Random real zeroes: one derivative.
- Random real zeroes: two derivatives.
- Sensitivity and superconcentration.