K. R. Parthasarathy (probabilist): Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous editNext edit →
Content deleted Content added
VisualWikitext
→‎Biography: +family.
Line 43: Line 43:


==Published work(s)==
==Published work(s)==
Among the books he has authored are:
Among the books authored by Parthasarathy include:
* K. R. Parthasarathy. [[Probability measure]]s on [[metric spaces]]. Vol. 352. [[American Mathematical Society]], 1967.
* K. R. Parthasarathy. [[Probability measure]]s on [[metric spaces]]. Vol. 352. [[American Mathematical Society]], 1967.
* [[Robin Lyth Hudson]] and K. R. Parthasarathy. "Quantum Ito's formula and stochastic evolutions." [[Communications in Mathematical Physics]] 93.3 (1984): 301–323.
* [[Robin Lyth Hudson]] and K. R. Parthasarathy. "Quantum Ito's formula and stochastic evolutions." [[Communications in Mathematical Physics]] 93.3 (1984): 301–323.
* K. R. Parthasarathy. An introduction to quantum stochastic calculus. Vol. 85. Springer, 1992.
* K. R. Parthasarathy. An introduction to quantum stochastic calculus. Vol. 85. Springer, 1992.
* K. R. Parthasarathy and [[Klaus Schmidt (mathematician)|Klaus Schmidt]]. "[[Positive definite kernel]]s, continuous tensor products, and [[central limit theorem]]s of [[probability theory]]" (series: [[Lecture Notes in Mathematics]]). (1972).
* K. R. Parthasarathy and [[Klaus Schmidt (mathematician)|Klaus Schmidt]]. "[[Positive definite kernel]]s, continuous tensor products, and [[central limit theorem]]s of [[probability theory]]" (series: [[Lecture Notes in Mathematics]]). (1972).
* {{Cite book |last=Parthasarathy |first=K. R. |url=https://books.google.ca/books?hl=en&lr=&id=640bAgAAQBAJ&oi=fnd&pg=PA1&dq=K.+R.+Parthasarathy&ots=kKrDnffA-X&sig=gePrRCky7bATaTxtIUTfvwF2cZA&redir_esc=y#v=onepage&q=K.%20R.%20Parthasarathy&f=false |title=Probability Measures on Metric Spaces |date=2005 |publisher=American Mathematical Soc. |isbn=978-0-8218-3889-1 |language=en}}
* {{Cite book |last=Parthasarathy |first=K. R. |url=https://books.google.ca/books?hl=en&lr=&id=jfJdDwAAQBAJ&oi=fnd&pg=PP10&dq=K.+R.+Parthasarathy&ots=lZqp3gYNiF&sig=6iO02n1etd8HzsyuBZNaZQs97wI&redir_esc=y#v=onepage&q=K.%20R.%20Parthasarathy&f=false |title=Introduction to Probability and Measure |date=2005-05-15 |publisher=Springer |isbn=978-93-86279-27-9 |language=en}}
* {{Cite book |last=Parthasarathy |first=K. R. |url=https://books.google.ca/books?hl=en&lr=&id=Uet7CwAAQBAJ&oi=fnd&pg=PA10&dq=K.+R.+Parthasarathy&ots=WaeQi6woiw&sig=51lAamv2HUqyPFcEGFaJ5BL_7Ww&redir_esc=y#v=onepage&q=K.%20R.%20Parthasarathy&f=false |title=Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory |last2=Schmidt |first2=K. |date=2006-09-04 |publisher=Springer |isbn=978-3-540-37607-1 |language=en}}
* {{Cite book |last=Parthasarathy |first=K. R. |url=https://books.google.ca/books?hl=en&lr=&id=gW7Av36VoNMC&oi=fnd&pg=PP15&dq=K.+R.+Parthasarathy&ots=aoGX1EAinl&sig=dKx9kmnRpZQ3ZMq7hi-sAUINojg&redir_esc=y#v=onepage&q=K.%20R.%20Parthasarathy&f=false |title=An Introduction to Quantum Stochastic Calculus |date=1992 |publisher=Springer Science & Business Media |isbn=978-3-7643-2697-5 |language=en}}

Some of the papers published by Parthasarathy include:
* {{Cite journal |last=Hudson |first=R. L. |last2=Parthasarathy |first2=K. R. |date=1984-09-01 |title=Quantum Ito's formula and stochastic evolutions |url=https://doi.org/10.1007/BF01258530 |journal=Communications in Mathematical Physics |language=en |volume=93 |issue=3 |pages=301–323 |doi=10.1007/BF01258530 |issn=1432-0916}}
* {{Cite journal |last=Parthasarathy |first=K. R. |last2=Rao |first2=R. Ranga |last3=Varadarajan |first3=V. S. |date=1967 |title=Representations of Complex Semi-Simple Lie Groups and Lie Algebras |url=https://www.jstor.org/stable/1970351 |journal=Annals of Mathematics |volume=85 |issue=3 |pages=383–429 |doi=10.2307/1970351 |issn=0003-486X}}
* {{Cite journal |last=Parthasarathy |first=K R |date=2010-06-01 |title=What is a Gaussian state? |url=https://digitalcommons.lsu.edu/cosa/vol4/iss2/2 |journal=Communications on Stochastic Analysis |volume=4 |issue=2 |doi=10.31390/cosa.4.2.02 |issn=0973-9599}}
* {{Cite journal |last=Krishna |first=M. |last2=Parthasarathy |first2=K. R. |date=2002 |title=An Entropic Uncertainty Principle for Quantum Measurements |url=https://www.jstor.org/stable/25051432 |journal=Sankhyā: The Indian Journal of Statistics, Series A (1961-2002) |volume=64 |issue=3 |pages=842–851 |issn=0581-572X}}
* {{Cite journal |last=Parthasarathy |first=K. R. |last2=Ravindra |first2=G. |date=1976-01-01 |title=The strong perfect-graph conjecture is true for K1,3-free graphs |url=https://www.sciencedirect.com/science/article/pii/S0095895676800056 |journal=Journal of Combinatorial Theory, Series B |language=en |volume=21 |issue=3 |pages=212–223 |doi=10.1016/S0095-8956(76)80005-6 |issn=0095-8956}}
* {{Cite journal |last=Bhatia |first=Rajendra |last2=Parthasarathy |first2=K. R. |date=2000-03 |title=Positive Definite Functions and Operator Inequalities |url=http://doi.wiley.com/10.1112/S0024609399006797 |journal=Bulletin of the London Mathematical Society |language=en |volume=32 |issue=2 |pages=214–228 |doi=10.1112/S0024609399006797}}</ref>
* {{Cite journal |last=Hudson |first=R. L. |last2=Parthasarathy |first2=K. R. |date=1986-09-01 |title=Unification of fermion and Boson stochastic calculus |url=https://doi.org/10.1007/BF01210951 |journal=Communications in Mathematical Physics |language=en |volume=104 |issue=3 |pages=457–470 |doi=10.1007/BF01210951 |issn=1432-0916}}
* {{Cite journal |last=Parthasarathy |first=K. R. |last2=Nandakumar |first2=R. |date=1983-01-01 |title=Unique eccentric point graphs |url=https://www.sciencedirect.com/science/article/pii/0012365X83902716 |journal=Discrete Mathematics |language=en |volume=46 |issue=1 |pages=69–74 |doi=10.1016/0012-365X(83)90271-6 |issn=0012-365X}}
* {{Cite journal |last=Parthasarathy |first=K. R. |date=1988-01 |title=The passage from random walk to diffusion in quantum probability |url=https://www.cambridge.org/core/journals/journal-of-applied-probability/article/abs/passage-from-random-walk-to-diffusion-in-quantum-probability/81E368228CC84E822088FCB19235655B |journal=Journal of Applied Probability |language=en |volume=25 |issue=A |pages=151–166 |doi=10.2307/3214153 |issn=0021-9002}}
* {{Citation |last=Hudson |first=R. L. |title=Stochastic Dilations of Uniformly Continuous Completely Positive Semigroups |date=1984 |url=https://doi.org/10.1007/978-94-009-6484-6_6 |work=Positive Semigroups of Operators, and Applications |pages=353–378 |editor-last=Bratteli |editor-first=Ola |access-date=2023-06-25 |place=Dordrecht |publisher=Springer Netherlands |language=en |doi=10.1007/978-94-009-6484-6_6 |isbn=978-94-009-6484-6 |last2=Parthasarathy |first2=K. R. |editor2-last=Jørgensen |editor2-first=Palle E. T.}}
* {{Cite journal |last=Parthasarathy |first=K. R. |last2=Sengupta |first2=Ritabrata |date=2015-12 |title=From particle counting to Gaussian tomography |url=https://www.worldscientific.com/doi/abs/10.1142/S021902571550023X |journal=Infinite Dimensional Analysis, Quantum Probability and Related Topics |volume=18 |issue=04 |pages=1550023 |doi=10.1142/S021902571550023X |issn=0219-0257}}
* {{Cite journal |last=Parthasarathy |first=K |date=2005-05 |title=Extremal quantum states in coupled systems |url=https://linkinghub.elsevier.com/retrieve/pii/S0246020305000233 |journal=Annales de l'Institut Henri Poincare (B) Probability and Statistics |language=en |volume=41 |issue=3 |pages=257–268 |doi=10.1016/j.anihpb.2003.10.009}}
* {{Cite journal |last=Rajarama Bhat |first=B. V. |last2=Parthasarathy |first2=K. R. |date=1995 |title=Markov dilations of nonconservative dynamical semigroups and a quantum boundary theory |url=http://www.numdam.org/item/?id=AIHPB_1995__31_4_601_0 |journal=Annales de l'I.H.P. Probabilités et statistiques |language=en |volume=31 |issue=4 |pages=601–651 |issn=1778-7017}}</ref>
* Parthasarathy, K. R., Ranga Rao, R., & Varadhan, S. R. S. (1962). [https://community.ams.org/journals/tran/1962-102-02/S0002-9947-1962-0153041-7/S0002-9947-1962-0153041-7.pdf On the category of indecomposable distributions on topological groups. Transactions of the American Mathematical Society], 102(2), 200-217.
Chicago


==References==
==References==

Revision as of 20:29, 25 June 2023

K. R. Parthasarathy
Born(1936-06-25)25 June 1936
Madras, Madras Presidency, British India (now Chennai, Tamil Nadu, India)
Died14 June 2023(2023-06-14) (aged 86)
Delhi, India
Alma materRamakrishna Mission Vivekananda College, Indian Statistical Institute
Known forQuantum stochastic calculus
SpouseShyama Parthasarathy
Children2
AwardsShanti Swarup Bhatnagar Award
TWAS Prize
Scientific career
FieldsMathematics
InstitutionsIndian Statistical Institute
Doctoral advisorC. R. Rao

Kalyanapuram Rangachari Parthasarathy (25 June 1936 – 14 June 2023) was an Indian statistician who was professor emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus. Parthasarathy was the recipient the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Science in 1977 and the TWAS Prize in 1996.

Biography

Parthasarathy was born on 25 June 1936 at Madras,[1] into a modest but deeply religious Hindu Brahmin family.[2][3][4] He completed his early years of schooling in Thanjavur, before moving back to Madras to complete his schooling from P. S. School in the Mylapore neighborhood of the city.[5] He went on to study at the Ramakrishna Mission Vivekananda College, where he completed the B.A. (Honours) course in Mathematics, and moved to the Research and Training school at the Indian Statistical Institute, Kolkata, where he completed his Ph.D., under the supervision of C. R. Rao in 1962. He was one of the "famous four"[6] (the others were R. Ranga Rao, Veeravalli S. Varadarajan, and S. R. Srinivasa Varadhan) in ISI during 1956–1963. He was awarded the first Ph.D. degree of ISI.[3] He received the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Science in 1977 and the TWAS Prize in 1996.[7]

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 theoretical probability during his time at the Indian Statistical Institute.[8] He later worked at the Steklov Mathematical Institute, USSR Academy of Sciences (1962–63), as Lecturer where he collaborated with Andrey Kolmogorov.[9] During this time, he continued to focus on the foundations of probability theory.[8] Later he came to United Kingdom as Professor of Statistics in University of Sheffield (1964–68), University of Manchester (1968–70) and later at University of Nottingham where he collaborated with Robin Lyth Hudson on their pioneering work in quantum stochastic calculus.[4][10][11][12] Then he returned to India, and after a few years in Bombay University and the Indian Institute of Technology, Delhi, he came back in 1976 to the new Indian Statistical Institute, Delhi Centre and he stayed there until he retired in 1996.[3] He continued to remain as a professor emeritus at the institute until the early 2020s.[8]

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 quantum stochastic calculus, some of Parthasarathy's other research areas included quantum probability, foundations of quantum mechanics, information theory, stochastic processes, and group representations. He also served on many governmental committees.[8][5]

Published work(s)

Among the books authored by Parthasarathy include:

  • K. R. Parthasarathy. Probability measures on metric spaces. Vol. 352. American Mathematical Society, 1967.
  • Robin Lyth Hudson and K. R. Parthasarathy. "Quantum Ito's formula and stochastic evolutions." Communications in Mathematical Physics 93.3 (1984): 301–323.
  • K. R. Parthasarathy. An introduction to quantum stochastic calculus. Vol. 85. Springer, 1992.
  • K. R. Parthasarathy and Klaus Schmidt. "Positive definite kernels, continuous tensor products, and central limit theorems of probability theory" (series: Lecture Notes in Mathematics). (1972).
  • Parthasarathy, K. R. (2005). Probability Measures on Metric Spaces. American Mathematical Soc. ISBN 978-0-8218-3889-1.
  • Parthasarathy, K. R. (15 May 2005). Introduction to Probability and Measure. Springer. ISBN 978-93-86279-27-9.
  • Parthasarathy, K. R.; Schmidt, K. (4 September 2006). Positive Definite Kernels, Continuous Tensor Products, and Central Limit Theorems of Probability Theory. Springer. ISBN 978-3-540-37607-1.
  • Parthasarathy, K. R. (1992). An Introduction to Quantum Stochastic Calculus. Springer Science & Business Media. ISBN 978-3-7643-2697-5.

Some of the papers published by Parthasarathy include:

Chicago

References

  1. ^ Kalyanapuram Rangachari PARTHASARATY Archived 8 September 2014 at the Wayback Machine at mathunion.org
  2. ^ Parthasarathy, K. R. (1986). "From Information Theory to Quantum Mechanics" (PDF). The Craft of Probabilistic Modelling: A Collection of Personal Accounts. Applied Probability. 1. Springer: 235–249. doi:10.1007/978-1-4613-8631-5_16. ISBN 978-1-4613-8633-9.
  3. ^ a b c Kalyan Bidhan Sinha and B. V. Rajarama Bhat. "Professor K. R. Parthasarathy" (PDF). Louisiana State University.
  4. ^ a b "Conferring on him the degree of Doctor of Sciences". Chennai Mathematical Institute.
  5. ^ a b c "A Different Kind of Mind – Bhāvanā". Retrieved 25 June 2023.
  6. ^ Kalyan Bidhan Sinha and B. V. Rajarama Bhat. "Veeravalli S. Varadarajan" (PDF). Louisiana State University.
  7. ^ "Prizes and Awards". The World Academy of Sciences. 2016.
  8. ^ a b c d e f "Remembering K R Parthasarathy: A life in numbers". The Indian Express. 24 June 2023. Retrieved 25 June 2023.
  9. ^ "Professor KR Parthasarathy". Indian National Science Academy. Archived from the original on 1 September 2015. Retrieved 18 May 2013.
  10. ^ D Applebaum. "Robin Hudson's Pathless Path to Quantum Stochastic Calculus" (PDF). Archived from the original (PDF) on 4 March 2016.
  11. ^ Jinqiao Duan; Shunlong Luo; Caishi Wang (2010). Recent development in stochastic dynamics and stochastic analysis. World Scientific. p. preface-x. ISBN 978-9814277266.
  12. ^ K. R. Parthasarathy. "Quantum Stochastic Calculus". Archived from the original on 28 July 2012. Retrieved 27 April 2013.
  13. ^ 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

External links

Retrieved from "https://en.wikipedia.org/w/index.php?title=K._R._Parthasarathy_(probabilist)&oldid=1161913382"