Full Description
From 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.
Contents
Large 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.
