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

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Matematicheskie Zametki, 2008, Volume 83, Issue 6, Pages 880–898
DOI: https://doi.org/10.4213/mzm4839 (Mi mzm4839)

This article is cited in 20 scientific papers (total in 20 papers)

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

V. P. Maslov^a, V. E. Nazaikinskii^b

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

Full-text PDF (606 kB) Citations (20)

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

Abstract: We consider tuples

$\{N_{jk}\}$ ,

$j=1,2,\dots$ ,

$k=1,\dots,q_j$ , 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.

Received: 14.05.2008

English version:
Mathematical Notes, 2008, Volume 83, Issue 6, Pages 804–820
DOI: https://doi.org/10.1134/S000143460805026X

Bibliographic databases:

UDC: 519.2+531.19

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/mzm4839

https://doi.org/10.4213/mzm4839

https://www.mathnet.ru/eng/mzm/v83/i6/p880

Cycle of papers

On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. I
V. P. Maslov, V. E. Nazaikinskii
Mat. Zametki, 2008, 83:2, 232–263
On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. II
V. P. Maslov, V. E. Nazaikinskii
Mat. Zametki, 2008, 83:3, 381–401
On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. III
V. P. Maslov, V. E. Nazaikinskii
Mat. Zametki, 2008, 83:6, 880–898

This publication is cited in the following 20 articles:

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
Maslov V.P., “Negative energy, debts, and disinformation from the viewpoint of analytic number theory”, Russ. J. Math. Phys., 23:3 (2016), 355–368
V. P. Maslov, V. E. Nazaikinskii, “Disinformation Theory for Bosonic Computational Media”, Math. Notes, 99:6 (2016), 895–900
V. P. Maslov, V. E. Nazaikinskii, “Remark on the Notion of Optimal Data Compression in Information Theory”, Math. Notes, 99:4 (2016), 616–618
V. P. Maslov, V. E. Nazaikinskii, “Bose–Einstein Distribution as a Problem of Analytic Number Theory: The Case of Less than Two Degrees of Freedom”, Math. Notes, 100:2 (2016), 245–255
V. P. Maslov, V. E. Nazaikinskii, “On the Rate of Convergence to the Bose–Einstein Distribution”, Math. Notes, 99:1 (2016), 95–109
V. P. Maslov, V. E. Nazaikinskii, “Conjugate Variables in Analytic Number Theory. Phase Space and Lagrangian Manifolds”, Math. Notes, 100:3 (2016), 421–428
Maslov V.P., “Bubbles in the Negative Pressure Domain”, Russ. J. Math. Phys., 22:4 (2015), 483–490
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
V. P. Maslov, “Probability Distributions of Partition Theory in Number Theory Arising in Classical Thermodynamics and Economics”, Math. Notes, 98:4 (2015), 699–703
V. P. Maslov, “Jump in the Number of Collective Degrees of Freedom as a Phase Transition of the First Kind”, Math. Notes, 97:2 (2015), 230–242
Maslov V.P., “New global distributions in number theory and their applications”, J. Fixed Point Theory Appl., 8:1 (2010), 81–111
V. P. Maslov, “Thermodynamic equations of state with three defining constants”, Math Notes, 87:5-6 (2010), 728
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
V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Satisfying Two Linear Relations”, Math. Notes, 84:1 (2008), 73–99
V. P. Maslov, “Thermodynamics of Nanostructures”, Math. Notes, 84:4 (2008), 592–595
V. P. Maslov, “Transition to the Condensate State for Classical Gases and Clusterization”, Math. Notes, 84:6 (2008), 785–813
V. P. Maslov, “New distribution formulas for classical gas, clusters, and phase transitions”, Theoret. and Math. Phys., 157:2 (2008), 1577–1594
Maslov V.P., “New look at thermodynamics of gas and at clusterization”, Russ. J. Math. Phys., 15:4 (2008), 493–510
Maslov V.P., “On a new universal constant in ideal gas theory in a nanoporous medium”, Math. Notes, 84:3 (2008), 439–441

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

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