K. R. Parthasarathy (probabilist)
Kalyanapuram Rangachari Parthasarathy (25 June 1936 – 14 June 2023) was an Indian statistician who was professor emeritus at the
Biography
Parthasarathy was born on 25 June 1936 in
Parthasarathy then moved to Kolkata to attend the Research and Training school at the Indian Statistical Institute, where he completed his Ph.D., under the supervision of C. R. Rao in 1962. He was one of the "famous four" at ISI from 1956 to 1963, alongside R. Ranga Rao, Veeravalli S. Varadarajan, and S. R. Srinivasa Varadhan.[6] He was awarded the first Ph.D. degree of ISI.[3]
He received the
Parthasarathy was married to Shyama Parthasarathy. The couple had two sons.[5] Parthasarathy died in Delhi on 14 June 2023, at the age of 86.[8]
Research
Parthasarathy started his work on
After returning to India, he spent a few years at
Parthasarathy is the namesake of Kostant–Parthasarathy–Ranga Rao–Varadarajan determinants along with Bertram Kostant, R. Ranga Rao and Veeravalli S. Varadarajan which they introduced in 1967.[13] He collaborated with Ranga Rao and Varadarajan to write a paper on representation theory of lie groups referred to as the PRV paper that was the foundation for further research on this topic.[8]
In addition to pioneering contributions to
Published works
Books
- K. R. Parthasarathy. metric spaces. Vol. 352. American Mathematical Society, 1967.
- Parthasarathy, K. R.; Schmidt, K. (1972). Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory. Springer.
- Parthasarathy, K. R. (1992). An Introduction to Quantum Stochastic Calculus. Springer Science & Business Media. ISBN 978-3-7643-2697-5.[14]
- Parthasarathy, K. R. (2005). Probability Measures on Metric Spaces. American Mathematical Soc. ISBN 978-0-8218-3889-1.
- Parthasarathy, K. R. (2005). Introduction to Probability and Measure. Springer. ISBN 978-93-86279-27-9.
Papers
- Hudson, R. L.; Parthasarathy, K. R. (1984). "Quantum Ito's formula and stochastic evolutions". Communications in Mathematical Physics. 93 (3): 301–323. S2CID 122848524.
- Parthasarathy, K. R.; Rao, R. Ranga; Varadarajan, V. S. (1967). "Representations of Complex Semi-Simple Lie Groups and Lie Algebras". Annals of Mathematics. 85 (3): 383–429. JSTOR 1970351.
- Parthasarathy, K R (2010). "What is a Gaussian state?". Communications on Stochastic Analysis. 4 (2). ISSN 0973-9599.
- Krishna, M.; Parthasarathy, K. R. (2002). "An Entropic Uncertainty Principle for Quantum Measurements". Sankhyā: The Indian Journal of Statistics, Series A (1961-2002). 64 (3): 842–851. JSTOR 25051432.
- Bhatia, Rajendra; Parthasarathy, K. R. (2000). "Positive Definite Functions and Operator Inequalities". Bulletin of the London Mathematical Society. 32 (2): 214–228. S2CID 14312608.</ref>
- Hudson, R. L.; Parthasarathy, K. R. (1986). "Unification of fermion and Boson stochastic calculus". Communications in Mathematical Physics. 104 (3): 457–470. S2CID 123132851.
- Parthasarathy, K. R. (1988). "The passage from random walk to diffusion in quantum probability". Journal of Applied Probability. 25 (A): 151–166. S2CID 119819984.
- Hudson, R. L.; Parthasarathy, K. R. (1984). Bratteli, Ola; Jørgensen, Palle E. T. (eds.). Stochastic Dilations of Uniformly Continuous Completely Positive Semigroups. Dordrecht: Springer Netherlands. pp. 353–378. )
- Parthasarathy, K. R.; Sengupta, Ritabrata (2015). "From particle counting to Gaussian tomography". Infinite Dimensional Analysis, Quantum Probability and Related Topics. 18 (4): 1550023–1550497. S2CID 73693185.
- Parthasarathy, K (2005). "Extremal quantum states in coupled systems". Annales de l'Institut Henri Poincaré B. 41 (3): 257–268. S2CID 14210453.
- Rajarama Bhat, B. V.; Parthasarathy, K. R. (1995). "Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory". Annales de l'Institut Henri Poincaré B. 31 (4): 601–651. ISSN 1778-7017.
- Parthasarathy, K. R., Ranga Rao, R., & Varadhan, S. R. S. (1962). On the category of indecomposable distributions on topological groups. Transactions of the American Mathematical Society, 102(2), 200-217.
References
- ^ Kalyanapuram Rangachari PARTHASARATY Archived 8 September 2014 at the Wayback Machine at mathunion.org
- )
- ^ a b c Kalyan Bidhan Sinha and B. V. Rajarama Bhat. "Professor K. R. Parthasarathy" (PDF). Louisiana State University.
- ^ a b "Conferring on him the degree of Doctor of Sciences". Chennai Mathematical Institute.
- ^ a b c "A Different Kind of Mind – Bhāvanā". Retrieved 25 June 2023.
- ^ Kalyan Bidhan Sinha and B. V. Rajarama Bhat. "Veeravalli S. Varadarajan" (PDF). Louisiana State University.
- ^ "Prizes and Awards". The World Academy of Sciences. 2016.
- ^ a b c d e f "Remembering K R Parthasarathy: A life in numbers". The Indian Express. 24 June 2023. Retrieved 25 June 2023.
- ^ "Professor KR Parthasarathy". Indian National Science Academy. Archived from the original on 1 September 2015. Retrieved 18 May 2013.
- ^ D. Applebaum. "Robin Hudson's Pathless Path to Quantum Stochastic Calculus" (PDF). Archived from the original (PDF) on 4 March 2016.
- ISBN 978-9814277266.
- ^ K. R. Parthasarathy. "Quantum Stochastic Calculus". Archived from the original on 28 July 2012. Retrieved 27 April 2013.
- ^ K. R. Parthasarathy, R. Ranga Rao, and Veeravalli S. Varadarajan. "Representations of complex semi-simple Lie groups and Lie algebras". The Annals of Mathematics 85.3 (1967): 383–429
- ^ a b "Books by K. R. Parthasarathy".
External links
- Kalyanapuram Rangachari Parthasarathy at the Mathematics Genealogy Project
- K. R. Parthasaraty at Indian Statistical Institute (Delhi Center)
- https://web.archive.org/web/20120728070024/http://www.mathunion.org/Publications/Bulletins/39/parthasarathy.ps
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