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Uspekhi Mat. Nauk, 1997, Volume 52, Issue 2(314), Pages 139–146 (Mi umn823)  

This article is cited in 21 scientific papers (total in 22 papers)


Scientific papers in honour of R. L. Dobrushin
Limit distribution of the energy of a quantum ideal gas from the viewpoint of the theory of partitions of natural numbers

A. M. Vershik

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

DOI: https://doi.org/10.4213/rm823

Full text: PDF file (202 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1997, 52:2, 379–386

Bibliographic databases:

UDC: 519.2
MSC: 82B10, 11Pxx
Received: 15.09.1996

Citation: A. M. Vershik, “Limit distribution of the energy of a quantum ideal gas from the viewpoint of the theory of partitions of natural numbers”, Uspekhi Mat. Nauk, 52:2(314) (1997), 139–146; Russian Math. Surveys, 52:2 (1997), 379–386

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bogachev, LV, “On approximation of convex functions via random polygons”, Doklady Akademii Nauk, 364:3 (1999), 299  mathnet  mathscinet  zmath  isi
    2. Senya Shlosman, “Geometric variational problems of statistical mechanics and of combinatorics”, J Math Phys (N Y ), 41:3 (2000), 1364  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. G. Freiman, A. M. Vershik, Yu. V. Yakubovich, “A Local Limit Theorem for Random Strict Partitions”, Theory Probab Appl, 44:3 (2000), 453  mathnet  crossref  mathscinet  isi  elib
    4. A. M. Vershik, Yu. V. Yakubovich, “The limit shape and fluctuations of random partitions of naturals with fixed number of summands”, Mosc. Math. J., 1:3 (2001), 457–468  mathnet  mathscinet  zmath  elib
    5. S. B. Shlosman, “The Wulff construction in statistical mechanics and combinatorics”, Russian Math. Surveys, 56:4 (2001), 709–738  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Vershik, A, “Two lectures on the asymptotic representation theory and statistics of Young diagrams”, Asymptotic Combinatorics With Applications To Mathematical Physics, 1815 (2003), 161  crossref  mathscinet  zmath  isi
    7. Yu. V. Yakubovich, “On the coincidence of limit shapes for integer partitions and compositions, and a slicing of Young diagrams”, J. Math. Sci. (N. Y.), 131:2 (2005), 5569–5577  mathnet  crossref  mathscinet  zmath  elib  elib
    8. Vershik, A, “Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions”, Communications in Mathematical Physics, 261:3 (2006), 759  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Alain Comtet, Satya N Majumdar, Stéphane Ouvry, “Integer partitions and exclusion statistics”, J Phys A Math Theor, 40:37 (2007), 11255  crossref  mathscinet  zmath  isi  scopus
    10. 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
    11. 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
    12. Erlihson, MM, “Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case”, Annales de l Institut Henri Poincare-Probabilites et Statistiques, 44:5 (2008), 915  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. Maslov V.P., “New global distributions in number theory and their applications”, Journal of Fixed Point Theory and Applications, 8:1 (2010), 81–111  crossref  mathscinet  zmath  isi  scopus
    14. Bogachev L.V., Zarbaliev S.M., “Universality of the Limit Shape of Convex Lattice Polygonal Lines”, Ann Probab, 39:6 (2011), 2271–2317  crossref  mathscinet  zmath  isi  elib  scopus
    15. Yakubovich Yu., “Ergodicity of Multiplicative Statistics”, J. Comb. Theory Ser. A, 119:6 (2012), 1250–1279  crossref  mathscinet  zmath  isi  elib  scopus
    16. V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Russian Math. Surveys, 69:1 (2014), 165–179  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. Bogachev L.V., “Unified Derivation of the Limit Shape For Multiplicative Ensembles of Random Integer Partitions With Equiweighted Parts”, 47, no. 2, 2015, 227–266  crossref  mathscinet  zmath  isi  scopus  scopus
    18. 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
    19. Maslov V.P., “Large negative numbers in number theory, thermodynamics, information theory, and human thermodynamics”, Russ. J. Math. Phys., 23:4 (2016), 510–528  crossref  mathscinet  zmath  isi  scopus
    20. 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
    21. V. P. Maslov, “The Relationship between the Fermi–Dirac Distribution and Statistical Distributions in Languages”, Math. Notes, 101:4 (2017), 645–659  mathnet  crossref  crossref  mathscinet  isi  elib
    22. Fatkullin I., Slastikov V., “Limit Shapes For Gibbs Ensembles of Partitions”, J. Stat. Phys., 172:6 (2018), 1545–1563  crossref  mathscinet  zmath  isi  scopus
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