Syllabus for Math 468, Section E1
This is a special topics course in the theory of Large Deviations.
Provisional Schedule
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Some ``Large Deviations'' problems
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Laplace asymptotics
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Some definitions and basic results
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Definitions
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Contraction Principle
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Varadhan's Lemma
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A simple form of Cramer's Theorem on the real line
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Schilder's Theorem
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The Gartner-Ellis theorem
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Donsker-Varadhan type results (including Sanov's theorem)
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Hydrodynamical Limits
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Wulff shape
References:
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A. Dembo and O. Zeitouni, Large Deviations Techniques, Jones and
Bartlett, 1993.
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J.-D. Deuschel and D. W. Stroock, Large Deviations, Academic Press,
1989.
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M. I. Freidlin and A. D. Wentzell, Random Perturbations of Dynamical
Systems, Springer, 1984
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D.W. Stroock, An Introduction to the Theory of Large Deviations,
Springer, 1984
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S.R.S. Varadhan, Large Deviations, SIAM, 1984.
Grading Policy: There will be two possibilities. Option 1 is to submit
answers to some homework questions which will irregularly be given. Option
2 is to give a 1-hour explanation of some moderately current research paper.
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Richard Sowers
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