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We construct a family of Markov processes with continuous sample trajectories on an infinite-dimensional space, the Thoma simplex.
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S. Kerov, G. Olshanski, and A. Vershik, Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. Comptes Rendus Acad. Sci. Paris, Sér. I, 316
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S. Kerov and G. Olshanski, Polynomial functions on the set of Young diagrams. Comptes Rendus Acad. Sci. Paris, Sér. I, 319
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I. G. Macdonald, Symmetric functions and Hall polynomials, 2nd edition, Oxford University Press, 1995
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S. V. Kerov, The boundary of Young lattice and random Young tableaux. In: Formal power series and algebraic combinatorics (New Brunswick, NJ, 1994) DIMACS Ser. Discrete Math. Theoret. Comput. Sci. 24
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K. W. J. Kadell, The Selberg-Jack symmetric functions. Adv. Math. 130
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A. Okounkov and G. Olshanski, Shifted Jack polynomials, binomial formula, and applications. Math. Research Lett. 4
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S. Kerov, G. Olshanski, and A. Vershik, Harmonic analysis on the infinite symmetric group. Invent. Math. 158
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A. Lascoux and J.-Y. Thibon, Vertex operators and the class algebras of symmetric groups. J. Math. Sci. (N. Y.) 121
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A. Borodin and G. Olshanski, Z-measures on partitions and their scaling limits. European J. Comb. 26
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S. V. Kerov, Interlacing measures. In: Kirillov’s seminar on representation theory (G. Olshanski, ed.), Amer. Math. Soc. Transl. Ser. 2, 181
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S. Kerov, A. Okounkov, G. Olshanski, The boundary of Young graph with Jack edge multiplicities. Intern. Math. Res. Notices (1998), no. 4, 173–199; arXiv: q-alg/9703037
1998
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A. Borodin, Multiplicative central measures on the Schur graph. J. Math. Sci. (New York) 96
1999
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A. Borodin and G. Olshanski, Distributions on partitions, point processes and the hypergeometric kernel. Comm. Math. Phys. 211
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A. Borodin and G. Olshanski. Harmonic functions on multiplicative graphs and interpolation polynomials. Electronic J. Comb. 7
2000
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S. V. Kerov, Anisotropic Young diagrams and Jack symmetric functions. Funct. Anal. Appl. 34
2000
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A. Borodin Harmonic analysis on the infinite symmetric group and the Whittaker kernel. St. Petersburg Math. J. 12
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J. Fulman, Stein’s method and Plancherel measure of the symmetric group. Trans. Amer. Math. Soc. 357
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A. Okounkov, The uses of random partitions. In: XIVth International Congress on Mathematical Physics, World Sci. Publ., Hackensack, NJ, 2005, pp. 379–403
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A. N. Sergeev and A. P. Veselov, Generalised discriminants, deformed Calogero–Moser–Sutherland operators and super-Jack polynomials. Adv. Math. 192
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A. Borodin and G. Olshanski, Markov processes on partitions. Prob. Theory and Related Fields 135
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A. Borodin and G. Olshanski, Stochastic dynamics related to Plancherel measure on partitions. In: Representation Theory, Dynamical Systems, and Asymptotic Combinatorics (V. Kaimanovich and A. Lodkin, eds). Amer. Math. Soc. Translations, Series 2: Advances in the Mathematical Sciences, 217
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P. J. Forrester and S. O. Warnaar, The importance of the Selberg integral. Bull. Amer. Math. Soc. 45
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J. Fulman, Stein’s method and random character ratios. Trans. Amer. Math. Soc. 360
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2009
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