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S.R. Srinivasa Varadhan

S.R. Srinivasa Varadhan. Born in Madras (now Chennai), India, January 2, 1940. B.Sc. Presidency College, 1959 Ph.D. Indian Institute of Statistics, 1963 From 1963 at the Courant Institute of Mathematical Sciences at New York University. Scientific Work.

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S.R. Srinivasa Varadhan

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  1. S.R. Srinivasa Varadhan • Born in Madras (now Chennai), India, January 2, 1940. • B.Sc. Presidency College, 1959 • Ph.D. Indian Institute of Statistics, 1963 • From 1963 at the Courant Institute of Mathematical Sciences at New York University

  2. Scientific Work • Varadhan is a probabilist, often working on problems from mathematical physics with tools from partial differential equations • Areas: Martingale problems and diffusion theory, large particle systems, hydrodynamical limits, random walks in random media, quantum field theory....

  3. Large Deviations ...... but the citation particularly emphasizes his work on large deviations

  4. Probability theory From games of chance to large deviations

  5. Games of chance • Geronimo Cardano (1501-1576): “De ludo alea” (published 1663) • Blaise Pascal (1623-1662) and Pierre de Fermat (1601-1656), letter correspondence 1654 • First textbook: Christian Huygens: “De ratiociniis in Alea Ludo”, 1657

  6. Limit laws • The Law of Large Numbers: Jakob Bernoulli (1654-1705), “Ars Conjectandi”, published 1713 • The Central Limit Theorem: Abraham De Moivre (1667-1754), “The Doctrine of Chances” (2nd edition), 1738

  7. The Law of Large Numbers • Coin tossing:

  8. The Central Limit Theorem • Bell shaped curves - mean and variance

  9. Large Deviations • Harald Cramér (1893-1985)

  10. Importance of Large Deviations: • Insurance companies: Probability of a “bad year” • Constructions: Impact on waves on oil drilling platforms in the North Sea • Networks: Probability that a network will break down due to overload during peak hours

  11. Varadhan’s Contribution: • Turned Large Deviation theory into an extremely smooth, powerful and efficient tool in many areas of mathematics and related fields. His Large Deviation Principle succinctly sums up what is needed to apply the technique.

  12. Subtle effects • Large deviation results are much more subtle than classical limit laws — the nature of each individual experiment becomes important

  13. Techniques • Varadhan’s work is a tour de force combining techniques from probability theory, nonlinear analysis, partial differential equations and functional analysis.

  14. Applications • The Large Deviation Principle has applications in statistics, insurance, finance, statistical physics, hydrodynamics, partial differential equations..... • And, of course, in many parts of probability theory

  15. Other contributions by Varadhan: • Martingale problems (with D.W. Stroock) • Hydrodynamical limits • Random walks in random media • Etc., etc.

  16. A worthy winner • Varadhan is very highly regarded in the probability community, not only for his scientific results, but also for his style. He is friendly, accessible, but with high standards. His emphasis is always on ideas and general methods, rather than technicalities.

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