Normal convergence for random partitions with multiplicative measures

Zh. Su

Teoriâ veroâtnostej i ee primeneniâ, Tome 59 (2014) no. 1, pp. 97-129

Bibliographie

[1] Andrews G. E., The Theory of Partitions, v. 2, Encyclopedia of Mathematics and Its Applications, Addison-Wesley, Reading, MA, 1976 | MR | Zbl

[2] Billingsli P., Skhodimost veroyatnostnykh mer, Nauka, M., 1977, 352 pp. | MR

[3] Bloch S., Okounkov A., “The character of the infinite wedge representation”, Adv. Math., 149:1 (2000), 1–60 | DOI | MR | Zbl

[4] Bogachev L. V., Su Z. G., “Gaussian fluctuations of Young diagrams under the Plancherel measure”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 463 (2007), 1069–1080 | DOI | MR | Zbl

[5] Borodin A., Okounkov A., Olshanski G., “Asymptotics of Plancherel measures for symmetric groups”, J. Amer. Math. Soc., 13:3 (2000), 481–515 | DOI | MR | Zbl

[6] de Bruijn N. G., Asymptotic Methods in Analysis, North-Holland Publishing, Amsterdam, 1958 | Zbl

[7] Erdös P., Lehner J., “The distribution of the number of summands in the partition of a positive integer”, Duke Math. J., 8 (1941), 335–345 | DOI | MR

[8] Erlihson M. M., Granovsky B. L., “Limit shapes of Gibbs distributions on the set of integer partitions: The expansive case”, Ann. Inst. H. Poincare Probab. Statist., 44:5 (2008), 915–945 | DOI | MR | Zbl

[9] Frame J. S., de B. Robinson G., Thrall R. M., “The hook graphs of the symmetric groups”, Canadian J. Math., 6 (1954), 316–324 | DOI | MR | Zbl

[10] Fristedt B., “The structure of random partitions of large integers”, Trans. Amer. Math. Soc., 2:2 (1993), 703–735 | DOI | MR | Zbl

[11] Frobenius G., “Uber die charactere der symmetrischen gruppe”, Sitzungsber. Preuss. Akad. Berlin, 1903, 328–358 | Zbl

[12] Gikhman I. I., Skorokhod A. V., Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1965, 656 pp. | MR

[13] Ivanov V., Olshanski G., Kerov's central limit theorem for the Plancherel measure on Young diagrams, Kluwer Academic Publishers, Dordrecht, 2002 | MR

[14] Johansson K., “Discrete orthogonal polynomial ensembles and the Plancherel measure”, Ann. Math., 153:1 (2001), 259–296 | DOI | MR | Zbl

[15] Kerov S., “Gaussian limit for the Plancherel measure of the symmetric group”, C. R. Acad. Sci. Paris Ser. I Math., 316:4 (1993), 303–308 | MR | Zbl

[16] Logan B. F., Shepp L. A., “A variational problem for random Young tableaux”, Adv. Math., 26:2 (1977), 206–222 | DOI | MR | Zbl

[17] Okounkov A., “Random matrices and random permutations”, Internat. Math. Res. Notices, 20 (2000), 1043–1095 | DOI | MR | Zbl

[18] Okounkov A., “The uses of random partitions”, XIVth International Congress on Mathematical Physics, ed. Jean-Claude Zambrini, World Sci. Publ., 2005, 379–403 | MR | Zbl

[19] Petrov V. V., Summy nezavismykh sluchainykh velichin, Nauka, M., 1972, 416 pp. | MR

[20] Pittel B., “On a likely shape of the random Ferrers digram”, Adv. Appl. Math., 18:4 (1997), 432–488 | DOI | MR | Zbl

[21] Pittel B., “On the distribution of the number of Young tableaux for a uniformly random diagram”, Adv. Appl. Math., 29:2 (2002), 184–214 | DOI | MR | Zbl

[22] Szalay M., Turán P., “On some problems of the statistical theory of partitions with applications to characters of the symmetric group. I; II; III”, Acta Math. Acad. Sci. Hungar., 29 (1997), 361–379 ; 381–392 ; 32 (1978), 129–155 | DOI | MR | MR | DOI | MR | Zbl

[23] Vershik A. M., “Statistical mechanics of combinatorial partitions, and their limit shapes”, Funct. Anal. Appl., 30:2 (1996), 90–105 | DOI | MR | Zbl

[24] Vershik A. M., “Limit shapes of typical geometric configurations and their applications”, J. Math. Sci., 119:2 (2004), 165–177 | DOI | MR

[25] Vershik A. M., Kerov S., “Asymptotics of the Plancherel measure of the symmetric group and the limit form of Young tableaux”, Soviet Math. Dokl., 18 (1977), 527–531 | Zbl

[26] Vershik A. M., Yakubovich Yu., “Fluctuations of the maximal particle energy of the quantum ideal gas and random partitions”, Comm. Math. Phys., 261:3 (2006), 795–769 | DOI | MR