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 Mat. Zametki, 2016, Volume 99, Issue 1, paper published in the English version journal (Mi mz11089)

Papers published in the English version of the journal

On the Rate of Convergence to the Bose–Einstein Distribution

V. P. Maslovab, V. E. Nazaikinskiibc

a National Research University Higher School of Economics, Moscow, Russia
b Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia
c Moscow Institute of Physics and Technology (State University), Moscow, Russia

Abstract: For a system of identical Bose particles sitting at integer energy levels with the probabilities of microstates given by a multiplicative measure with $\ge2$ degrees of freedom, we estimate the probability of the sequence of occupation numbers to be close to the Bose–Einstein distribution as the total energy tends to infinity. We show that a convergence result earlier proved by A. M. Vershik [Functional Anal. Appl. 30 (2), 95–105 (1996)] is a corollary of our theorems.

Keywords: Bose–Einstein distribution, multiplicative measure, convergence, cumulative distribution, limit distribution.

DOI: https://doi.org/10.1134/S0001434616010107

English version:
Mathematical Notes, 2016, 99:1, 95–109

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Citation: V. P. Maslov, V. E. Nazaikinskii, “On the Rate of Convergence to the Bose–Einstein Distribution”, Math. Notes, 99:1 (2016), 95–109

Citation in format AMSBIB
\Bibitem{MasNaz16} \by V.~P.~Maslov, V.~E.~Nazaikinskii \paper On the Rate of Convergence to the Bose–Einstein Distribution \jour Math. Notes \yr 2016 \vol 99 \issue 1 \pages 95--109 \mathnet{http://mi.mathnet.ru/mz11089} \crossref{https://doi.org/10.1134/S0001434616010107} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3486109} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000373228900010} \elib{http://elibrary.ru/item.asp?id=26983576} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962449770} 

• http://mi.mathnet.ru/eng/mz11089
• https://doi.org/10.1134/S0001434616010107

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. P. Maslov, “Analytic Number Theory and Disinformation”, Math. Notes, 100:4 (2016), 568–578
2. V. P. Maslov, S. Yu. Dobrokhotov, V. E. Nazaikinskii, “Volume and Entropy in Abstract Analytic Number Theory and Thermodynamics”, Math. Notes, 100:6 (2016), 828–834
3. V. P. Maslov, “Negative energy, debts, and disinformation from the viewpoint of analytic number theory”, Russ. J. Math. Phys., 23:3 (2016), 355–368
4. D. S. Minenkov, V. E. Nazaikinskii, V. L. Chernyshev, “On the limit shape of elements of an arithmetic semigroup with an exponentially growing counting function of basis elements”, Dokl. Math., 95:3 (2017), 226–229