Sergei Chobanyan

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Sergei Chobanyan
Native name	Սերգեյ Չոբանյան
Born	(1942-04-04) April 4, 1942 Tbilisi, Georgian SSR, Soviet Union
🏳️ Citizenship	Soviet Union Georgia
🏫 Education	Tbilisi State University
💼 Occupation
Known for	Probability Distributions on Banach Spaces Maximal inequalities for rearrangements of summands

Sergei Akopovich Chobanyan (; ; also known as Sergo Chobanyan; born 4 April 1942) is a Georgian-Armenian mathematician working in functional analysis and probability theory. He is a co-author of the monograph Probability Distributions on Banach Spaces, a standard reference on probability in infinite-dimensional spaces, and is known for his work on the rearrangement of series in normed spaces.

Biography

Chobanyan was born on 4 April 1942 in Tbilisi. He graduated from Tbilisi State University in 1965, and from 1968 worked at the Institute of Computational Mathematics of the Georgian Academy of Sciences (the N. Muskhelishvili Institute of Computational Mathematics, later incorporated into Georgian Technical University). He served as a leading researcher there from 1989 to 2004, and from 2004 headed a department of the institute. He received the degree of Doctor of Physical and Mathematical Sciences in 1985 and the title of professor in 1996. His seventieth birthday was marked in 2012 at the Third International Conference of the Georgian Mathematical Union in Batumi.

According to the biographical encyclopedia Who is Who: Armenians, Chobanyan is a first cousin of the mechanician Karapet Chobanyan and of Martun Chobanyan.

Research

Probability in Banach spaces

With Nicholas Vakhania and Vazha Tarieladze, Chobanyan wrote Probability Distributions on Banach Spaces, published in Russian by Nauka in 1985 and in English translation by D. Reidel in 1987 in the Soviet Series of the Mathematics and Its Applications collection, translated by Wojbor Woyczynski. The book treats measures and random elements in Banach spaces, covariance operators, characteristic functionals, sums of independent random elements and limit theorems. It remains in use as a general reference for probability measures on infinite-dimensional spaces and was reissued in softcover in 2011.

Rearrangements of series

Chobanyan has worked extensively on the effect of rearranging the summands of a series in a normed space, a circle of problems connected with the structure of the set of sums of a conditionally convergent series and with Kolmogorov's rearrangement conjecture on systems of convergence for orthogonal series. In a 1985 paper in Matematicheskii Sbornik he described the structure of the set of sums of a conditionally convergent series in a normed space. He subsequently obtained general maximal inequalities relating the convergence of rearrangements of a series to the convergence of the same series with signs attached, results that are cited in the literature on the subject alongside those of Adriano Garsia, Bernard Maurey and Gilles Pisier.

In joint work with collaborators at Michigan State University, he applied these methods to establish conditions under which the strong law of large numbers holds under rearrangements of a sequence of random variables.

Selected publications

• Vakhania, N. N.; Tarieladze, V. I.; Chobanyan, S. A. (1987). Probability Distributions on Banach Spaces. Mathematics and Its Applications (Soviet Series). Translated by Wojbor A. Woyczynski. Dordrecht: D. Reidel. ISBN 978-90-277-2496-0. Search this book on
• Chobanyan, S. A. (1985). Структура множества сумм условно сходящегося ряда в нормированном пространстве [Structure of the set of sums of a conditionally convergent series in a normed space]. Matematicheskii Sbornik (in русский). 128(170) (1(9)): 50–65.
• Chobanyan, S. A. (1994). "Convergence a.s. of rearranged random series in Banach space and associated inequalities". Probability in Banach Spaces, 9. Progress in Probability. 35. Boston: Birkhäuser. pp. 3–29. Search this book on
• Chobanyan, S.; Levental, S.; Mandrekar, V. (2004). "Prokhorov Blocks and Strong Law of Large Numbers Under Rearrangements". Journal of Theoretical Probability. 17 (3): 647–672. doi:10.1023/B:JOTP.0000040292.52298.fd.
• Chobanyan, Sergei; Levental, Shlomo (2022). "Maximum inequalities in rearrangements of orthogonal series". Georgian Mathematical Journal. 29 (6): 823–831. doi:10.1515/gmj-2022-2181.

References

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