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**Collected papers. Volume I: Limit theorems, review articles. Edited by Rajendra Bhatia, Abhay Bhatt and K. R. Parthasarathy.**
*(English)*
Zbl 1311.82002

Berlin: Springer; New Dehli: Hindustan Book Agency (ISBN 978-3-642-33544-0/hbk; 978-3-642-33231-9/set; 978-93-80250-39-7/set). xiv, 532 p. (2012).

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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 of a young 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 topics in probability, analysis and physics, and collaborated with several distinguished mathematicians. These collected works contain all his research papers over the half-century from 1962 to early 2012.

The articles of this volume will be reviewed individually.

For Volumes II, III and IV see [Zbl 1311.82003; Zbl 1308.82002; Zbl 1311.82004].

Indexed articles:

Varadhan, S. R. S., Autobiography: S. R. S. Varadhan, 1-13 [Zbl 1316.01022]

Varadhan, S. R. S., Introduction, 15-21 [Zbl 1316.82005]

Bhatia, Rajendra (ed.); Bhatt, Abhay (ed.); Poithasarathy, K. R. (ed.), Prize citations, 22-24 [Zbl 1316.01016]

Stroock, Daniel W., Varadhan’s work on diffusion theory, 25-31 [Zbl 1316.60120]

Stroock, Daniel W., Varadhan’s work on large deviations, 32-36 [Zbl 1316.60036]

Rezakhanlou, Fraydoun, Varadhan’s work on large deviations and homogenization, 37-49 [Zbl 1316.82013]

Quastel, Jeremy; Yau, Horng-Tzer, Varadhan’s work on hydrodynamical limits, 50-57 [Zbl 1316.82025]

Williams, David, Book review of: D. W. Stroock and S. R. S. Varadhan, Multidimensional diffusion processes, 58-65 [Zbl 1316.00020]

Varadhan, S. R. S., Limit theorems for sums of independent random variables with values in a Hilbert space, 69-94 [Zbl 1316.60046]

Parthasarathy, K. R.; Ranga Rao, R.; Varadhan, S. R. S., On the category of indecomposable distributions on topological groups, 95-112 [Zbl 1316.60024]

Parthasarathy, K. R.; Ranga Rao, R.; Varadhan, S. R. S., Probability distributions on locally compact abelian groups, 113-145 [Zbl 1316.60025]

Parthasarathy, K. R.; Varadhan, S. R. S., Extension of stationary stochastic processes, 146-152 [Zbl 1316.60051]

Varadhan, S. R. S., Limit theorems in probability, 153-157 [Zbl 1316.60047]

Papanicolaou, G. C.; Varadhan, S. R. S., A limit theorem with strong mixing in Banach space and two applications to stochastic differential equations, 158-185 [Zbl 1316.60013]

Stroock, Daniel W.; Varadhan, S. R. S., Limit theorems for random walks on Lie groups, 186-203 [Zbl 1316.60016]

Papanicolaou, G. C.; Stroock, Daniel W.; Varadhan, S. R. S., Martingale approach to some limit theorems, 204-325 [Zbl 1316.60097]

Kipnis, C.; Varadhan, S. R. S., Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions, 326-344 [Zbl 1316.60112]

Gubner, John A.; Gopinath, B.; Varadhan, S. R. S., Bounding functions of Markov processes and the shortest queue problem, 345-363 [Zbl 1316.60137]

Digernes, Trond; Varadarajan, V. S.; Varadhan, S. R. S., Finite approximations to quantum systems, 364-391 [Zbl 1316.47065]

Varadhan, S. R. S., Self diffusion of a tagged particle in equilibrium for asymmetric mean zero random walk with simple exclusion, 392-404 [Zbl 1316.60148]

Sethuraman, Sunder; Varadhan, S. R. S.; Yau, Horng-Tzer, Diffusive limit of a tagged particle in asymmetric simple exclusion processes, 405-439 [Zbl 1316.60147]

Sethuraman, S.; Varadhan, S. R. S., A martingale proof of Dobrushin’s theorem for non-homogeneous Markov chains, 440-454 [Zbl 1316.60114]

Varadhan, S. R. S., Diffusion processes, 459-476 [Zbl 1316.60125]

Varadhan, S. R. S., Stochastic analysis and applications, 477-485 [Zbl 1316.60086]

Varadhan, S. R. S., Large deviations and entropy, 486-501 [Zbl 1316.60085]

Varadhan, S. R. S., Large deviations, 502-524 [Zbl 1316.60006]

Varadhan, S. R. S., The role of weak convergence in probability theory, 525-532 [Zbl 1316.60033]

### MSC:

82-06 | Proceedings, conferences, collections, etc. pertaining to statistical mechanics |

01A75 | Collected or selected works; reprintings or translations of classics |

82B31 | Stochastic methods applied to problems in equilibrium statistical mechanics |

60F05 | Central limit and other weak theorems |