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Mat. Zametki, 2008, Volume 83, Issue 6, Pages 880–898 (Mi mz4839)  

This article is cited in 12 scientific papers (total in 12 papers)

On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. III

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: We consider tuples $\{N_{jk}\}$, $j=1,2,…$, $k=1,…,q_j$, of nonnegative integers such that
$$ \sum_{j=1}^\infty\sum_{k=1}^{q_j} jN_{jk}\le M. $$
Assuming that $q_j\sim j^{d-1}$, $1<d<2$, we study how the probabilities of deviations of the sums $\sum_{j=j_1}^{j_2}\sum_{k=1}^{q_j} N_{jk}$ from the corresponding integrals of the Bose–Einstein distribution depend on the choice of the interval $[j_1,j_2]$.

Keywords: Bose–Einstein distribution, Legendre transform, random variable, Gram matrix, Euler–Maclaurin formula, strict convexity

DOI: https://doi.org/10.4213/mzm4839

Full text: PDF file (606 kB)
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English version:
Mathematical Notes, 2008, 83:6, 804–820

Bibliographic databases:

UDC: 519.2+531.19
Received: 14.05.2008

Citation: V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. III”, Mat. Zametki, 83:6 (2008), 880–898; Math. Notes, 83:6 (2008), 804–820

Citation in format AMSBIB
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    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, “Thermodynamics of Nanostructures”, Math. Notes, 84:4 (2008), 592–595  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. 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
    4. V. P. Maslov, “New distribution formulas for classical gas, clusters, and phase transitions”, Theoret. and Math. Phys., 157:2 (2008), 1577–1594  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. Maslov V.P., “New look at thermodynamics of gas and at clusterization”, Russ. J. Math. Phys., 15:4 (2008), 493–510  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Maslov V.P., “On a new universal constant in ideal gas theory in a nanoporous medium”, Math. Notes, 84:3 (2008), 439–441  crossref  mathscinet  zmath  isi  elib  scopus
    7. Maslov V., “Dequantization, Statistical Mechanics and Econophysics”, Tropical and Idempotent Mathematics, Contemporary Mathematics, 495, ed. Litvinov G. Sergeev S., Amer Mathematical Soc, 2009, 239–279  crossref  mathscinet  zmath  isi
    8. Maslov V.P., “New global distributions in number theory and their applications”, J. Fixed Point Theory Appl., 8:1 (2010), 81–111  crossref  mathscinet  zmath  isi  scopus
    9. Maslov V.P., “Bubbles in the Negative Pressure Domain”, Russ. J. Math. Phys., 22:4 (2015), 483–490  crossref  mathscinet  zmath  isi  scopus
    10. Maslov V.P., “a New Distribution Corresponding To Thermodynamics in Supercritical and Subcritical Regions and in the Region of Negative Pressure”, Dokl. Math., 91:3 (2015), 379–383  crossref  mathscinet  zmath  isi  elib  scopus
    11. 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  mathnet  crossref  crossref  mathscinet  isi  elib
    12. Maslov V.P., “Negative energy, debts, and disinformation from the viewpoint of analytic number theory”, Russ. J. Math. Phys., 23:3 (2016), 355–368  crossref  mathscinet  zmath  isi  elib  scopus
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