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Mat. Zametki, 2008, Volume 83, Issue 2, Pages 232–263 (Mi mz4418)  

This article is cited in 36 scientific papers (total in 36 papers)

On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. 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: We consider the mathematical problem of the allocation of indistinguishable particles to integer energy levels under the condition that the number of particles can be arbitrary and the total energy of the system is bounded above. Systems of integer as well as fractional dimension are considered. The occupation numbers can either be arbitrary nonnegative integers (the case of “Bose particles”) or lie in a finite set $\{0,1,dots,R\}$ (the case of so-called parastatistics; for example, $R=1$ corresponds to the Fermi–Dirac statistics). Assuming that all allocations satisfying the given constraints are equiprobable, we study the phenomenon whereby, for large energies, most of the allocations tend to concentrate near the limit distribution corresponding to the given parastatistics.

Keywords: Bose-Einstein statistics, parastatistics, system of fractional dimension, cumulative distribution, convergence, limit distribution


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English version:
Mathematical Notes, 2008, 83:2, 211–237

Bibliographic databases:

UDC: 519.2+531.19
Received: 11.01.2008

Citation: V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. I”, Mat. Zametki, 83:2 (2008), 232–263; Math. Notes, 83:2 (2008), 211–237

Citation in format AMSBIB
\by V.~P.~Maslov, V.~E.~Nazaikinskii
\paper On the Distribution of Integer Random Variables Related by a Certain Linear Inequality.~I
\jour Mat. Zametki
\yr 2008
\vol 83
\issue 2
\pages 232--263
\jour Math. Notes
\yr 2008
\vol 83
\issue 2
\pages 211--237

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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 Related by a Certain Linear Inequality. II”, Math. Notes, 83:3 (2008), 345–363  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by Two Linear Inequalities: I”, Math. Notes, 83:4 (2008), 512–529  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. P. Maslov, “Solution of the Gibbs Paradox in the Framework of Classical Mechanics (Statistical Physics) and Chrystalizations of the Gas $C_{60}$”, Math. Notes, 83:5 (2008), 716–722  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. V. P. Maslov, “Taking into Account the Interaction between Particles in the New Nucleation Theory, Quasiparticles, Quantization of Vortices, and the Two-Particle Distribution Function”, Math. Notes, 83:6 (2008), 790–803  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. V. P. Maslov, V. E. Nazaikinskii, “On the Distribution of Integer Random Variables Related by a Certain Linear Inequality. III”, Math. Notes, 83:6 (2008), 804–820  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    14. Maslov V., “Dequantization, statistical mechanics and econophysics”, Tropical and idempotent mathematics, Contemp. Math., 495, ed. Litvinov G. Sergeev S., Amer. Math. Soc., Providence, RI, 2009, 239–279  crossref  mathscinet  zmath  isi
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    19. V. P. Maslov, “Phase transitions in real gases and ideal Bose gases”, Theoret. and Math. Phys., 167:2 (2011), 654–667  mathnet  crossref  crossref  mathscinet  adsnasa  isi
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    21. Maslov V.P. Maslov A.V. Maslova T.V., “New paradigm in thermodynamics and its connection with economics and linguistics”, Russ. J. Math. Phys., 18:3 (2011), 329–337  crossref  mathscinet  zmath  isi  elib  scopus
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    24. V. P. Maslov, T. V. Maslova, “Unbounded probability theory and its applications”, Theory Probab. Appl., 57:3 (2013), 444–467  mathnet  crossref  crossref  mathscinet  isi  elib  elib
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