A. M. Vershik, G. A. Freiman, Yu. V. Yakubovich, “A local limit theorem for random strict partitions”, Teor. Veroyatnost. i Primenen., 44:3 (1999), 506–525; Theory Probab. Appl., 44:3 (2000), 453

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Teoriya Veroyatnostei i ee Primeneniya, 1999, Volume 44, Issue 3, Pages 506–525
DOI: https://doi.org/10.4213/tvp801 (Mi tvp801)

This article is cited in 28 scientific papers (total in 29 papers)

A local limit theorem for random strict partitions

A. M. Vershik^a, G. A. Freiman^b, Yu. V. Yakubovich^a

^a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
^b The Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Israel

Full-text PDF (1013 kB) Citations (29)

DOI: https://doi.org/10.4213/tvp801

Abstract: We consider a set of partitions of natural number $n$ on distinct summands with uniform distribution. We investigate the limit shape of the typical partition as $n\to\infty$, which was found in [A. M. Vershik, Funct. Anal. Appl., 30 (1996), pp. 90–105], and fluctuations of partitions near its limit shape. The geometrical language we use allows us to reformulate the problem in terms of random step functions (Young diagrams). We prove statements of local limit theorem type which imply that joint distribution of fluctuations in a number of points is locally asymptotically normal. The proof essentially uses the notion of a large canonical ensemble of partitions.

Keywords: partition, Young diagram, large ensemble of partitions, local limit theorem.

Received: 15.09.1998

English version:
Theory of Probability and its Applications, 2000, Volume 44, Issue 3, Pages 453–468
DOI: https://doi.org/10.1137/S0040585X97977719

Bibliographic databases:

Language: Russian

Citation: A. M. Vershik, G. A. Freiman, Yu. V. Yakubovich, “A local limit theorem for random strict partitions”, Teor. Veroyatnost. i Primenen., 44:3 (1999), 506–525; Theory Probab. Appl., 44:3 (2000), 453–468

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tvp801

https://doi.org/10.4213/tvp801

https://www.mathnet.ru/eng/tvp/v44/i3/p506

This publication is cited in the following 29 articles:

Jean C. Peyen, Leonid V. Bogachev, Paul P. Martin, “Boltzmann distribution on “short” integer partitions with power parts: Limit laws and sampling”, Advances in Applied Mathematics, 159 (2024), 102739
Guozheng Dai, Zhonggen Su, “On the Fluctuations for Multiplicative Ensembles of Random Integer Partitions with Equiweighted Parts”, Front. Math, 18:1 (2023), 197
Bogachev L.V., Yakubovich Yu.V., “Limit Shape of Minimal Difference Partitions and Fractional Statistics”, Commun. Math. Phys., 373:3 (2020), 1085–1131
Corwin I., Parekh Sh., “Limit Shape of Subpartition-Maximizing Partitions”, J. Stat. Phys., 180:1-6, SI (2020), 597–611
DeSalvo S., Pak I., “Limit Shapes Via Bijections”, Comb. Probab. Comput., 28:2 (2019), 187–240
V. P. Maslov, “The Relationship between the Fermi–Dirac Distribution and Statistical Distributions in Languages”, Math. Notes, 101:4 (2017), 645–659
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., “Large negative numbers in number theory, thermodynamics, information theory, and human thermodynamics”, Russ. J. Math. Phys., 23:4 (2016), 510–528
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, “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, “Conjugate Variables in Analytic Number Theory. Phase Space and Lagrangian Manifolds”, Math. Notes, 100:3 (2016), 421–428
V. P. Maslov, V. E. Nazaikinskii, “Disinformation Theory for Bosonic Computational Media”, Math. Notes, 99:6 (2016), 895–900
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 81
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 93
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 1
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 111
Tadahisa Funaki, SpringerBriefs in Probability and Mathematical Statistics, Lectures on Random Interfaces, 2016, 29
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
Funaki T., Sasada M., Sauer M., Xie B., “Fluctuations in an Evolutional Model of Two-Dimensional Young Diagrams”, Stoch. Process. Their Appl., 123:4 (2013), 1229–1275
Dan Beltoft, Cédric Boutillier, Nathanaël Enriquez, “Random Young Diagrams in a Rectangular Box”, Mosc. Math. J., 12:4 (2012), 719–745

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

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