RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2008, Volume 83, Issue 4, Pages 559–580 (Mi mz4576)  

This article is cited in 6 scientific papers (total in 6 papers)

On the Distribution of Integer Random Variables Related by Two Linear Inequalities: I

V. P. Maslova, V. E. Nazaikinskiib

a M. V. Lomonosov Moscow State University, Faculty of Physics
b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Abstract: The authors' two preceding papers deal with the problem on the allocation of indistinguishable particles to positive integer energy levels under the condition that the total energy of the system is bounded above by some constant $M$. The estimates proved there imply that, for large $M$, most of the allocations concentrate near a limit distribution (which is the Bose–Einstein distribution, provided that the particles obey the corresponding statistics). The present paper continues this trend of research by considering the case in which not only the total energy is constrained but also the overall number of particles is specified. We study both the Bose and the Gibbs distribution and analyze the phenomenon whereby the Bose distribution passes into the Gibbs distribution in the limit as the number of particles is relatively small.

Keywords: Bose–Einstein statistics, Boltzmann–Gibbs statistics, cumulative distribution, entropy, allocation of particles

DOI: https://doi.org/10.4213/mzm4576

Full text: PDF file (601 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2008, 83:4, 512–529

Bibliographic databases:

UDC: 519.2+531.19
Received: 25.03.2008

Citation: V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by Two Linear Inequalities: I”, Mat. Zametki, 83:4 (2008), 559–580; Math. Notes, 83:4 (2008), 512–529

Citation in format AMSBIB
\Bibitem{MasNaz08}
\by V.~P.~Maslov, V.~E.~Nazaikinskii
\paper On the Distribution of Integer Random Variables Related by Two Linear Inequalities:~I
\jour Mat. Zametki
\yr 2008
\vol 83
\issue 4
\pages 559--580
\mathnet{http://mi.mathnet.ru/mz4576}
\crossref{https://doi.org/10.4213/mzm4576}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2431622}
\zmath{https://zbmath.org/?q=an:1154.60076}
\transl
\jour Math. Notes
\yr 2008
\vol 83
\issue 4
\pages 512--529
\crossref{https://doi.org/10.1134/S0001434608030255}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000255998600025}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-43749117082}


Linking options:
  • http://mi.mathnet.ru/eng/mz4576
  • https://doi.org/10.4213/mzm4576
  • http://mi.mathnet.ru/eng/mz/v83/i4/p559

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Satisfying Two Linear Relations”, Math. Notes, 84:1 (2008), 73–99  mathnet  crossref  crossref  mathscinet  isi  elib
    2. V. P. Maslov, “Transition to the Condensate State for Classical Gases and Clusterization”, Math. Notes, 84:6 (2008), 785–813  mathnet  crossref  crossref  mathscinet  isi
    3. Маслов В.П., “Новая концепция процесса нуклеации”, ТМФ, 156:1 (2008), 159–160  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. Maslov V., “Dequantization, Statistical Mechanics and Econophysics”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, eds. Litvinov G., Sergeev S., Amer Mathematical Soc, 2009, 239–279  crossref  mathscinet  zmath  isi
    5. Maslov V.P., “The Relationship Between the Van-der-Waals Model and the Undistinguishing Statistics of Objectively Distinguishable Objects. the New Parastatistics”, Russ. J. Math. Phys., 21:1 (2014), 99–111  crossref  mathscinet  zmath  isi  elib  scopus
    6. Wang X., Luo X., Zhang M., Guan X., “Distributed Detection and Isolation of False Data Injection Attacks in Smart Grids Via Nonlinear Unknown Input Observers”, Int. J. Electr. Power Energy Syst., 110 (2019), 208–222  crossref  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:447
    Full text:101
    References:79
    First page:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019