# S. R. Srinivasa Varadhan

SR Srinivasa Varadhan ( Sathamangalam Ranga Iyengar Srinivasa Varadhan, born January 2, 1940 in Chennai) is a Tamil- American probabilists and statisticians.

## Life and work

Varadhan's father was a school teacher of mathematics. He studied in Chennai (formerly Madras ), University ( Presidency College ), received his bachelor 's degree in 1959 and his master's degree in 1960 and his doctorate in 1963 at the then leading Indian Statistical Institute, the Indian Statistical Institute ( ISI) in Kolkata at CR Rao. Fellow of him with whom he worked closely at that time, were R. Ranga Rao and KR Parthasarathy ( with VS Varadarajan, they were the Famous Four at ISI called ). After working for a year with Varadarajan on Lie groups ( from which, however no publications resulted ), he returned to the Statistics and went in 1963 to the Courant Institute in New York, where he was from 1966 to 1968 Assistant Professor, 1968-1972 Associate Professor and as of 1972 had a full professorship. Even then, he remained at the Courant Institute, where he is Professor of Mathematics and Frank J. Gould Professor of Science. 1980 to 1984 and 1992 to 1994 he was Director of the Institute. 1976/7 he was a visiting professor at Stanford University, in 1972 at the Mittag-Leffler Institute in Stockholm and 1991/ 92 at the Institute for Advanced Study in Princeton.

In his dissertation Convolution Properties of Distributions on topological groups ( for Andrei Kolmogorov as a foreign expert acted ), he expanded the central limit theorem in abstract spaces with infinite dimensions. At the Courant Institute, he developed with Daniel Stroock new methods for the study of Markov processes, which was reflected in the joint book Multidimensional Diffusion Processes of 1979. Also in the 1960s, began working with Monroe D. Donsker, leading to a general theory of large deviations (Large Deviations ) resulted in stochastic processes, gave 1937 first precise estimates for the probability of the Swede Harald Cramér. The theory was in his work Asymptotic probabilities and differential equations ( Communications in Pure and Applied Mathematics Bd.19, 1966, p.261 -286 ) and in their joint work Asymptotic evaluation of Certain Markov Process expectations for large time ( 4 parts, Communications set out in Pure and Applied Mathematics Bd.28, 1975, p.1 -47, p.279 -301, Bd.29, 1976, S.389 -461, Bd.36, 1983, p.183 -212 ). His theory has applications in fields such as quantum field theory, quantitative finance, population dynamics, statistical physics.

Varadhan also worked with Maozheng Guo and George Papanicolaou over macroscopic ( " hydrodynamic " ) limits of systems of many interacting particles.

Varadhan is married (his wife is a professor at New York University ) and has two sons, one of whom 2001 in the attack on the World Trade Center died.

## Awards

In 1996 he received the Leroy P. Steele Prize of the American Mathematical Society ( the prize money he established a hospital in Tambaram ), 1994 the Birkhoff Prize and the 2007 Abel Prize " for his fundamental contributions to probability theory and in particular for creating a unified theory large deviations (large deviations ) ". 1970/2 he was Alfred P. Sloan Fellow and Guggenheim Fellow 1984-5. Varadhan was Invited Speaker at the International Congress of Mathematicians 1978 ( Some problems of large Deviations ) and 1994 ( Plenary Lecture: Entropy methods in hydrodynamic scaling ). He is a member of the National Academy of Sciences of the United States and since 1998 a Fellow of the Royal Society. Since 2004 he is member of the Indian Academy of Sciences. In the same year he was made an honorary doctor of his old Institute ISI. In 2008 he was awarded the Padma Bhushan. In 2010 he received the National Medal of Science. He is a Fellow of the American Mathematical Society.