# Talk:Gaussian measure

Gaussian measures are the natural starting point for various Gaussian random processes (and fields). However, we have no article on Gaussian measures, and a rather obsolete article on Gaussian processes.

"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." [L]

"The modern theory of Gaussian measures lies at the intersection of the theory of random processes, functional analysis, and mathematical physics and is closely connected with diverse applications in quantum field theory, statistical physics, financial mathematics, and other areas of sciences. The study of Gaussian measures combines ideas and methods from probability theory, nonlinear analysis, geometry, linear operators, and topological vector spaces in a beautiful and nontrivial way." [B, Preface]

"Gaussian processes have a rich, detailed and very well understood general theory, which makes them beloved by theoreticians. In applications [...] it is important to have specific, explicit formulae that allow one to predict, to compare theory with experiment, etc. As we shall see [...] it will be only for Gaussian (and related [...]) fields that it is possible to derive such formulae in the setting of excursion sets." [AT]

[B] | V.I. Bogachev, "Gaussian measures", AMS (1998). MR1642391 Zbl 0913.60035 |

[L] | R. Latała, "On some inequalities for Gaussian measures", Proceedings of the International Congress of Mathematicians (2002), 813-822. MR1957087 Zbl 1015.60011 |

[AT] | R.J. Adler, J.E. Taylor, "Random fields and geometry", Springer (2007). MR2319516 Zbl 1149.60003 |

--Boris Tsirelson 22:12, 14 June 2012 (CEST)

**How to Cite This Entry:**

Gaussian measure.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Gaussian_measure&oldid=27023