Syllabus for Math 468, Section G1

• Instructor: Richard Sowers
• Office: 107 Altgeld 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 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.

Provisional Schedule

• 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
• 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.

Grading Policy