Math/Stat 833 Topics in Probability Spring 2013: Large Deviations and Gibbs Measures

Meetings: MWF 2:25-3:15, Van Vleck B129
Instructor: Timo Seppäläinen
Office: 419 Van Vleck
Telephone: 263-2812
E-mail: seppalai at math dot wisc dot edu

Lecture notes

The lecture notes have become a book manuscript and are no longer available from this course page.


Homework assignments will be posted here. Be sure to check the latest version of the notes to match the numbers with the correct exercises.

Spring 2013 Schedule

Further recommended materials

If you wish to read beyond the lecture notes, here are some suggestions.

Description of the course

Large deviation theory is an area of probability that seeks to quantify chances of extremely rare behavior, for example the kind that falls outside the central limit theorem. It has its origins in early probability and statistical mechanics. A unified formulation emerged in the 1960's especially through the work of S. Varadhan, who received the Abel Prize ("Nobel Prize of mathematics") for this and other achievements in 2007.

There are applications in various fields such as engineering, especially queueing theory, statistics and economics. Notions of entropy appear naturally in descriptions of these small probabilities.

Gibbs measures are probability measures that describe random systems in multidimensional space and possess a natural spatial Markovian property. They arose in the context of statistical physics.

This course intends to cover

Prerequisites for this course can be quite minimal. Measure theory and some advanced probability will be used, but the prerequisites needed can be covered quickly at the beginning.

There are a number of books on these topics. No textbook purchase is required. The instructor will use his own manuscript for an introductory text.