Description
Book SynopsisFrom 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 reputation as 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 I includes the introductory material, the papers on limit theorems and review articles.
Table of ContentsAutobiography: S. R. S. Varadhan.- Introduction: S. R. S. Varadhan.- Prize Citations.- Diffusion Theory by Daniel W. Stroock. - Large Deviations by Daniel W. Stroock.- Large Deviation and Homogenization by Fraydoun Rezakhanlou.- Varadhan's Work on Hydrodynamical Limits by Jeremy Quastel and Horng-Tzer Yau.- Book Review: Multidimensional Diffusion Processes by D. W. Stroock and S. R. S. Varadhan.- Limit Theorems: Limit theorems for sums of independent random variables with values in a Hilbert space.- On the category of indecomposable distributions on topological groups.- Probability distributions on locally compact abelian groups.- Extension of stationary stochastic processes.- Limit theorems in probability.- A limit theorem with strong mixing in Banach space and two applications to stochastic differential equations.- Limit theorems for random walks on Lie groups.- Martingale approach to some limit theorems.- Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions.- Bounding functions of Markov processes and the shortest queue problem.- Finite approximations to quantum systems.- Self-diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion.- Diffusive limit of a tagged particle in asymmetric simple exclusion processes.- A martingale proof of Dobrushin's theorem for non-homogeneous Markov chains.- Review Articles.- Diffusion processes, Stochastic processes: theory and methods.- Stochastic analysis and applications.- Large deviations and entropy, Entropy.- The role of weak convergence in probability theory.
