Boris Tsirelson

Boris Tsirelson, Oberwolfach 2005

Boris S. Tsirelson , Russian Борис Цирельсон (born May 4, 1950 in Leningrad ; † January 21, 2020 in Basel ), also cited by Cirelson , was a Russian-Israeli mathematician . He was a professor at Tel Aviv University and dealt with functional analysis , quantum theory and stochastic processes .

life and work

As a student, Tsirelson attended a group supervised by Vladimir Lifschitz and Alexander Kruglow for students gifted in mathematics (this also included Vyatcheslav Kharlamov , Serguey Kislyakov and Alex Reyman ). He received his doctorate from Ildar Ibragimov at the University of Leningrad in 1975 ( General properties of bounded Gaussian processes and related questions )

He found a counterexample in the theory of Banach spaces , published in 1974. The space named after him was the first real example of a non-classical Banach space.

With Anatoli Werschik , he investigated novel constructions of product spaces from probability spaces and Hilbert spaces and thus the introduction of new variants of noise (Black Noise).

A counterexample in the theory of stochastic differential equations is named after him (Tsirelson's equation). In 1974 he proved an isoperimetric inequality for Gaussian measures and the following, for example, theorems about the probability distribution of the norm of random vectors.

Building on the ideas of Anatoly Werschik (who dealt with the classification of filterings in the early 1970s and found that they are not all isomorphic to one another), he constructed non-standard filterings into stochastic processes (such as the tossing of a coin with an equal probability for heads and number). They found that standard filterings (according to Werschik) were not stable with an equivalent change in the probability measures; in particular, with Brownian movement such changes resulted in filterings that did not correspond to a Brownian process. In doing so, he introduced a cosiness invariant and cozy filtrations . Tsirelson came to similar results in the Walsh trials.

He also dealt with quantum computer science and quantum theory and examined the maximum correlation of distant events (maximum violation of a Bell inequality ) in quantum mechanics, answering a problem by Anatoly Werschik . He found an upper bound for it, known as the Tsirelson bound .

He also dealt with the classic limiting case of quantum mechanical systems with few degrees of freedom or their classic quantum mechanical correspondence (considered in the case that decoherence destroys the quantum mechanical interferences through thermal interaction with the environment) According to Tsirelson, a threshold value behavior results instead of the usual one considered limit value transition (Planck constant towards zero).

He also dealt with fault-tolerant cellular automata .

He was invited speaker at the International Congress of Mathematicians in Berlin 1998 ( Within and beyond the reach of Brownian innovation ). In 1976 he received the St. Petersburg Mathematical Society's Prize for Young Mathematicians .

Fonts

(Except those already quoted)

• Scaling limit, noise, stability , in: Wendelin Werner, Boris Tsirelson, Lectures on Probability Theory and Statistics, Ecole d'Eté de Probabilités de Saint-Flour XXXII - 2002 Lecture Notes in Mathematics 1840, 2004, 1–106
• with A. Vershik Examples of nonlinear continuous tensor products of measure spaces and non-Fock factorizations , Reviews in Mathematical Physics 10: 1, 81-145
• Nonclassical stochastic flows and continuous products , Probability Surveys 1, 2004, pp. 173-298

literature

• J. Azéma, M. Émery, M. Ledoux, M. Yor Séminaire des Probabilités XXXIII , Springer Verlag 1999 (therein essays by Walter Schachermayer, Emery, B. De Meyer zu Tsirelson, e.g. Schachermayer On certain probabilities equivalent to Wiener measure, d´après Dubins, Feldman, Smorodinsky and Tsirelson )

Web links

• Homepage
• Mathnet.ru

Individual evidence

1. ↑ Date of birth according to Albrecht Pietsch History of Banach Spaces and Linear Operators , Birkhäuser 2007
2. ↑ Entry prabook.com
3. ↑ Notice of death accessed on February 26, 2020
4. ↑ Boris Tsirelson in the Mathematics Genealogy Project (English)
5. ^ Tsirelson Not every Banach space contains an imbedding of or ${\displaystyle l_{p}}$ ${\displaystyle c_{0}}$ , Functional Analysis and its Applications 8, 1974, pp. 138-141. According to his own statements, the proof idea came to him from his study of the forcing method by Paul Cohen , whereby he had to remove references to Vitali Milman , in the Soviet Union in disgrace, memories of Tsirelson in his publication
6. ↑ PG Casazza, TJ Shura, Tsirelson's space , Lecture Notes in Math., Vol. 1363, Springer-Verlag, 1989
7. ↑ E. Odell, Th. Schlumprecht, Distortion and stabilized structure in Banach spaces; new geometric phenomena for Banach and Hilbert spaces , Proceedings of the International Congress of Mathematicians, Zurich 1994
8. ↑ Tsirelson An example of a stochastic differential equation having no strong solution , Theory Probab. Appl. 20, 1975, 416-418
9. ^ LCG Rogers, D. Williams Diffusion, Markov Processes and Martingales , Vol. 2, Wiley 1987, p. 155
10. ↑ Marc Yor Tsirel'son's equation in discrete time , probab. Theory Relat. Fields 91, 1992, pp. 135-152
11. ^ VN Sudakov, BS Tsirelson, Extremal properties of half-spaces for spherically invariant measures ", Journal of Soviet Mathematics 9, 1978, pp. 9-18
12. ↑ Tsirelson The density of the distribution of the maximum of a Gaussian process , Theory Probability Appl. 20, 1975, 847-856
13. ↑ Michel Èmery Espaces probabilisés filtrés: de la théorie de Vershik au mouvement brownien, via des idées de Tsirelson , Séminaire Bourbaki 882, 2000/2001, online ( Memento of the original from October 4, 2013 in the Internet Archive ) Info: The archive link became automatic used and not yet tested. Please check the original and archive link according to the instructions and then remove this notice. 
14. ↑ L. Dubins, J. Feldman, M. Smorodinski, Tsirelson Decreasing sequence of -fields and a measure change for Brownian motion ${\displaystyle \sigma }$ , Annals of Probability, 24, 1996, 882-904, Part 2 with Feldman 905-911, Online ( Memento of the original dated June 3, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. 
15. ↑ Michel Émery, Walter Schachermayer, On Vershik's Standardness criterion and Tsirelson's notion of cosines , Séminaire de probabilités de Strasbourg 35, 2001, Springer, Lecture Notes in Mathematics, pp. 265-305, pdf
16. ↑ Tsirelson Triple points: from non-Brownian filtrations to harmonic measures , GAFA (Geometric and Functional Analysis) 7, 1997, 1096-1142
17. ↑ Tsirelson Quantum generalizations of Bell's inequality , Lett. Math. Phys. 4, 1980, 93-100
18. ↑ LA Khalfin, BS Tsirelson, Quantum / classical correspondence in the light of Bell's inequalities , Foundations of Physics 22, 1992, 879-948, Tsirelson This non-axiomatizable quantum theory: From Hilbert's sixth problem to the recent viewpoint of Gell-Mann and Hartle , Preprint IHES 1994
19. ↑ Tsirelson Reliable storage of information in a system of unreliable components with local interactions , Lect. Notes Math. 653, Springer Verlag 1978, pp. 15-30