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OverviewFrom the Preface: Srinivasa Varadhan began his research career at the Indian Statistical Institute (ISI), Calcutta, where he started as a graduate student in 1959. His first paper appeared in Sankhyá, the Indian Journal of Statistics in 1962. Together with his fellow students V. S. Varadarajan, R. Ranga Rao and K. R. Parthasarathy, Varadhan began the study of probability on topological groups and on Hilbert spaces, and quickly gained an international reputation. At this time Varadhan realised that there are strong connections between Markov processes and differential equations, and in 1963 he came to the Courant Institute in New York, where he has stayed ever since. Here he began working with the probabilists Monroe Donsker and Marc Kac, and a graduate student named Daniel Stroock. He wrote a series of papers on the Martingale Problem and Diffusions together with Stroock, and another series of papers on Large Deviations together with Donsker. With this work Varadhan's reputationas one of the leading mathematicians of the time was firmly established. Since then he has contributed to several other areas of probability, analysis and physics, and collaborated with numerous distinguished mathematicians. Varadhan was awarded the Abel Prize in 2007. These Collected Works contain all his research papers over the half-century spanning 1962 to early 2012. Volume III includes the papers on large deviations. Full Product DetailsAuthor: S.R.S. Varadhan , Rajendra Bhatia , Abhay Bhatt , K.R. ParthasarathyPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2013 ed. Dimensions: Width: 16.00cm , Height: 3.00cm , Length: 25.00cm Weight: 1.152kg ISBN: 9783642335464ISBN 10: 3642335462 Pages: 630 Publication Date: 19 January 2013 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsLarge Deviations.- Asymptotic probabilities and differential equations.- On the behavior of the fundamental solution of the heat equation with variable coefficients .- Diffusion processes in a small time interval .- On a variational formula for the principal eigenvalue for operators with maximum principle.- Asymptotic evaluation of certain Markov process expectations for large time I.- Asymptotic evaluation of certain Markov process expectations for large time II.- Asymptotic evaluation of certain Wiener integrals for large time.- Asymptotics for the Wiener sausage.- Erratum: Asymptotics for the Wiener sausage.- Asymptotic evaluation of certain Markov process expectations for large time III.- On the principal eigenvalue of second-order elliptic differential operators.- On laws of the iterated logarithm for local times.- Some problems of large deviations.- On the number of distinct sites visited by a random walk.- A law of the iterated logarithm for total occupation times of transient Brownian motion.- Some problems of large deviations .- The polaron problem and large deviations.- Asymptotic evaluation of certain Markov process expectations for large time IV.- Asymptotics for the polaron.- Large deviations for stationary Gaussian processes.- Large deviations and applications.- Large deviations for non-interacting infinite-particle systems.- Some familiar examples for which the large deviation principle does not hold.- The large deviation principle for the Erdös-Rényi random graph.- Large deviations for random matrices. ReviewsS.R.S. Varadhan was awarded the Abel Prize in 2007.The citation for this award (https: //www.abelprize.no/c53862/binfil/download.php?tid=53801) ends with Varadhan's work has great conceptual strength and ageless beauty. His ideas have been hugely influential and will continue to stimulate further research for a long time. In 2011 Varadhan was named as a recipient of the National Medal of Science, the highest honor bestowed by the United States government on scientists and engineers. Varadhan is a member of the National Academy of Sciences, the American Academy of Arts and Sciences, the Royal Society and the Third World Academy of Sciences. He has been the recipient of other awards and honors, including the Birkhoff Prize (1994), the Margaret and Herman Sokol Award of NYU's Faculty of Arts and Science (1995), and the American Mathematical Society's Leroy Steele Prize (1996), an Alfred P. Sloan Fellowship, and a Guggenheim Fellowship. He is a fellow of the Institute of Mathematical Statistics and the Indian Academy of Sciences. "S.R.S. Varadhan was awarded the Abel Prize in 2007.The citation for this award (https: //www.abelprize.no/c53862/binfil/download.php?tid=53801) ends with ""Varadhan's work has great conceptual strength and ageless beauty. His ideas have been hugely influential and will continue to stimulate further research for a long time.""In 2011 Varadhan was named as a recipient of the National Medal of Science, the highest honor bestowed by the United States government on scientists and engineers. Varadhan is a member of the National Academy of Sciences, the American Academy of Arts and Sciences, the Royal Society and the Third World Academy of Sciences. He has been the recipient of other awards and honors, including the Birkhoff Prize (1994), the Margaret and Herman Sokol Award of NYU's Faculty of Arts and Science (1995), and the American Mathematical Society's Leroy Steele Prize (1996), an Alfred P. Sloan Fellowship, and a Guggenheim Fellowship. He is a fellow of the Institute of Mathematical Statistics and the Indian Academy of Sciences." Author Information"Rajendra Bhatia is Professor of Mathematics at the Indian Statistical Institute in New Delhi, India. He is the author of five books including ""Matrix Analysis"" and ""Positive Definite Matrices." Tab Content 6Author Website:Countries AvailableAll regions |
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