**Instructor:**Richard Sowers**Office:**107 Altgeld Hall**Phone:**(217) 333-6246**email:**r-sowers@math.uiuc.edu**Home page:**`https://math.uiuc.edu/~r-sowers`

(this syllabus can be found there)**Class meets:**Mondays, Wednes days, and Fridays 3-3:50 P.M. in 159 Altgeld Hall**Office Hours:**MWF: 2-3 and by appointment

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

- Lecture 1: Some ``Large Deviations'' problems
- Lecture 2: Laplace asymptotics
- Lecture 3: Some definitions and basic results
- Definitions
- Weak LDP's
- Exponential Tightness
- Contraction Principle
- Varadhan's Lemma

- Lecture 4: A simple form of Cramer's Theorem on the real line
- Lecture 5: Schilder's Theorem
- Lecture 6: Fun with Schilder's Theorem
- Lecture 7: Un soupcon d'analyze convexe
- Lecture 8: The Gartner-Ellis theorem
- Lecture 9: Advanced techniques
- Approximate Contraction principles
- LDP's for SDE's

- Projective Limits
- Sanov's Theorem

- Approximate Contraction principles
- Lecture 10: Donsker-Varadhan results

- 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.

Department of Mathematics

University of Illinois at Urbana-Champaign

1409 W Green St.

Urbana, IL 61801

r-sowers@math.uiuc.edu

(217) 333-6246