The asymptotics of plane partitions with fixed volumes of diagonal parts
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 26, Tome 487 (2019), pp. 68-77 Cet article a éte moissonné depuis la source Math-Net.Ru

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Determinantal representation for the generating function of plane partitions with fixed volumes of diagonal parts is investigated in limiting cases.
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N. Bogoliubov; C. Malyshev. The asymptotics of plane partitions with fixed volumes of diagonal parts. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 26, Tome 487 (2019), pp. 68-77. http://geodesic.mathdoc.fr/item/ZNSL_2019_487_a4/

[1] A. M. Vershik, “Statistical mechanics of combinatorial partitions, and their limit configurations”, Funct. Anal. Appl., 30 (1996), 90 | DOI | MR | Zbl

[2] G. E. Andrews, The Theory of Partitions, Cambridge University Press, Cambridge, 1998 | MR | Zbl

[3] D. M. Bressoud, Proofs and Confirmations. The Story of the Alternating Sign Matrix Conjecture, Cambridge University Press, Cambridge, 1999 | MR | Zbl

[4] R. P. Stanley, “The conjugate trace and trace of a plane partition”, J. Comb. Theor. A, 14 (1973), 53 | DOI | MR | Zbl

[5] E. Gansner, “The enumeration of plane partitions via the Burge correspondence”, Illinois J. Math., 25 (1981), 533 | DOI | MR | Zbl

[6] K. Krattenthaler, “Generating functions for plane partitions of a given shape”, Manuscripta Math., 69 (1990), 173 | DOI | MR | Zbl

[7] S. Melczer, G. Panova, R. Pemantle, Counting partitions inside a rectangle, arXiv: 1805.08375

[8] N. M. Bogoliubov, C. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70 (2015), 789 | DOI | MR | Zbl

[9] N. M. Bogoliubov, C. Malyshev, “The phase model and the norm-trace generating function of plane partitions”, J. Stat. Mech.: Theory and Experiment, 2018, 083101 | DOI | MR

[10] N. M. Bogoliubov, C. Malyshev, “The partition function of the four-vertex model in inhomogeneous external field and trace statistics”, J. Phys. A: Math. Theor., 52 (2019), 495002 | DOI | MR

[11] A. Okounkov, N. Reshetikhin, “Correlation function of Schur process with applications to local geometry of a random 3-dimensional Young diagram”, J. Amer. Math. Soc., 16 (2003), 581 | DOI | MR | Zbl

[12] N. M. Bogoliubov, C. Malyshev, “Correlation functions of $XX0$ Heisenberg chain, $q$-binomial determinants, and random walks”, Nucl. Phys. B, 879 (2014), 268 | DOI | MR | Zbl

[13] E. M. Wright, “Asymptotic partition formulae: (I) Plane partitions”, Quart. J. Math. Oxford Ser., 2 (1931), 177 | DOI

[14] R. Boyer, D. Parry, “Plane partition polynomial asymptotics”, The Ramanujan J., 37 (2015), 573 | DOI | MR | Zbl

[15] I. G. Macdonald, Symmetric functions and Hall polynomials, Clarendon Press, 1995 | MR | Zbl

[16] L. D. Faddeev, “Quantum completely integrable models of field theory”, Sov. Sci. Rev. Math. C, 1 (1980), 107 ; 40 Years in Mathematical Physics, World Sci. Ser. 20th Century Math., 2, World Sci., Singapore, 1995, 187–235 | MR | Zbl | DOI | MR

[17] V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press, Cambridge, 1993 | MR | Zbl

[18] T. Maeda, T. Nakatsu, K. Takasaki, T. Tamakoshi, “Five-dimensional supersymmetric Yang-Mills theories and random plane partitions”, JHEP, 2005 (2005), 056 | DOI | MR

[19] D. S. Moak, “The q-analogue of Stirling's formula”, Rocky Mountain J. Math., 14 (1984), 403 | DOI | MR | Zbl

[20] A. Klimyk, K. Schmudgen, Quantum Groups and their Representations, Springer-Verlag, Berlin–Heidelberg, 1997 | MR | Zbl

[21] E. T. Whittaker, G. N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge, 1996 | MR | Zbl

[22] E. E. Salpeter, “On Mayer's theory of cluster expansions”, Ann. Phys., 5 (1958), 183 | DOI | MR