Large Deviations

Math 595, Spring 2005
(Section LD, Course Reference Number 38183)


The study of rare events occupies an important part in many probabilistic analyses. While there are many types of rare events, the theory of exponentially small events appears frequently enough that it deserves special consideration. We will explore the circle of ideas known as large deviations, which studies the structure and transformations of such exponentially small events. We will start with a study of how quickly the law of large numbers holds, develop some general theories, such as the Gartner-Ellis theorem and the contraction principle, and then apply them in a number of ways. Along the way, we will understand connections with other areas of mathematics and engineering; for example, the connection between the exit problem and singularly perturbed PDE's, and the connection between empirical measures of Markov chains and entropy.

Provisional Schedule
References: Grading: Grades will be determined on the basis of homework (30%), a midterm (40%) and a final presentation (30%). My intention is that the final presentation be either on some part of Dembo-Zeitouni which we didn't cover in class, or on some research-level subject. Also, I intend to grade some of the homework by randomly selecting a person from class and having them do the homework at the board.

Instructor: Richard Sowers
Office: 347 Illini Hall
Phone: (217) 333-6246
email: r-sowers@math.uiuc.edu
Home page: https://faculty.math.illinois.edu/~r-sowers
Class meets: Mondays, Wednesdays, and Fridays 11-11:50 A.M. in 443 Altgeld Hall
Office Hours: MWF, 10-10:50