Asymptotics of Jack characters

Biane, 1998, Representations of symmetric groups and free probability, Adv. Math., 138, 126, 10.1006/aima.1998.1745 Borodin, 2005, Z-measures on partitions and their scaling limits, European J. Combin., 26, 795, 10.1016/j.ejc.2004.06.003 Brillinger, 1969, The calculation of cumulants via conditioning, Ann. Inst. Statist. Math., 21, 215, 10.1007/BF02532246 Burchardt Czyżewska-Jankowska, 2017, Bijection between oriented maps and weighted non-oriented maps, Electron. J. Combin., 24, 10.37236/6718 Diaconis, 1992, Eigen-analysis for some examples of the metropolis algorithm, Contemp. Math., 138, 99, 10.1090/conm/138/1199122 Dołęga, 2017, Top degree part in b-conjecture for unicellular bipartite maps, Electron. J. Combin., 24, 10.37236/6130 Dołęga, 2016, Gaussian fluctuations of Young diagrams and structure constants of Jack characters, Duke Math. J., 165, 1193, 10.1215/00127094-3449566 Dołęga, 2018, Gaussian fluctuations of Jack-deformed random Young diagrams, Probab. Theory Related Fields Dołęga, 2010, Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations, Adv. Math., 225, 81, 10.1016/j.aim.2010.02.011 Dołęga, 2014, Jack polynomials and orientability generating series of maps, Sém. Lothar. Combin., 70 Féray, 2011, Asymptotics of characters of symmetric groups related to Stanley character formula, Ann. of Math. (2), 173, 887, 10.4007/annals.2011.173.2.6 Féray, 2011, Zonal polynomials via Stanley's coordinates and free cumulants, J. Algebra, 334, 338, 10.1016/j.jalgebra.2011.03.008 Goulden, 1996, Connection coefficients, matchings, maps and combinatorial conjectures for Jack symmetric functions, Trans. Amer. Math. Soc., 348, 873, 10.1090/S0002-9947-96-01503-6 Ivanov, 2002, Kerov's central limit theorem for the Plancherel measure on Young diagrams, vol. 74, 93 Jack, 1970, A class of symmetric polynomials with a parameter, Proc. Roy. Soc. Edinburgh Sect. A, 69, 1 Kaneko, 1993, Selberg integrals and hypergeometric functions associated with jack polynomials, SIAM J. Math. Anal., 24, 1086, 10.1137/0524064 Kerov, 1993, Gaussian limit for the Plancherel measure of the symmetric group, C. R. Acad. Sci. Paris, Sér. I Math., 316, 303 Kerov, 2000, Anisotropic young diagrams and jack symmetric functions, Funct. Anal. Appl., 34, 41, 10.1007/BF02467066 Kerov, 1994, Polynomial functions on the set of Young diagrams, C. R. Acad. Sci. Paris, Sér. I Math., 319, 121 Lando, 2004, Graphs on Surfaces and Their Applications, vol. 141 Lassalle, 2008, A positivity conjecture for Jack polynomials, Math. Res. Lett., 15, 661, 10.4310/MRL.2008.v15.n4.a6 Lassalle, 2009, Jack polynomials and free cumulants, Adv. Math., 222, 2227, 10.1016/j.aim.2009.07.007 Matsumoto, 2008, Jack deformations of Plancherel measures and traceless Gaussian random matrices, Electron. J. Combin., 15, 10.37236/873 Sho Matsumoto, Piotr Śniady, Random strict partitions and random shifted tableaux, 2018, in preparation. Nakajima Okounkov, 1997, Shifted Jack polynomials, binomial formula, and applications, Math. Res. Lett., 4, 69, 10.4310/MRL.1997.v4.n1.a7 Śniady, 2006, Gaussian fluctuations of characters of symmetric groups and of Young diagrams, Probab. Theory Related Fields, 136, 263, 10.1007/s00440-005-0483-y Śniady Vershik, 1981, Asymptotic theory of the characters of a symmetric group, Funktsional. Anal. i Prilozhen., 15, 15