Syllabus for Math 468, Section E1

• Instructor: Richard Sowers
• Office: 227B Illini Hall
• Phone: (217) 333-6246
• email: r-sowers@math.uiuc.edu
• Home page:https://faculty.math.illinois.edu/~r-sowers (this syllabus can be found there)
• Class meets: Mondays, Wednes days, and Fridays 1-1:50 P.M. in 155 Altgeld Hall
• Office Hours: MWF: 12-1 and by appointment

This is a special topics course in the theory of Large Deviations.

• Some ``Large Deviations'' problems
• Laplace asymptotics
• Some definitions and basic results
• Definitions
• Contraction Principle
• Varadhan's Lemma
• A simple form of Cramer's Theorem on the real line
• Schilder's Theorem
• The Gartner-Ellis theorem
• Donsker-Varadhan type results (including Sanov's theorem)
• Hydrodynamical Limits
• Wulff shape

• A. Dembo and O. Zeitouni, Large Deviations Techniques, Jones and Bartlett, 1993.
• J.-D. Deuschel and D. W. Stroock, Large Deviations, Academic Press, 1989.
• M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical Systems, Springer, 1984
• D.W. Stroock, An Introduction to the Theory of Large Deviations, Springer, 1984
• S.R.S. Varadhan, Large Deviations, SIAM, 1984.