Outdated picture of Natalia Tsilevich Natalia Tsilevich

Senior researcher at
Laboratory of Representation Theory and Dynamical Systems
Steklov Institute of Mathematics at St.Petersburg
27 Fontanka, St.Petersburg 191023, Russia

Email: natalia <at> pdmi.ras.ru
Fax:  +7(812)3105377

Research papers

  • The serpantine representation of the infinite symmetric group and the basic representation of the affine Lie algebra $\widehat{sl}_2$ (with A.M.Vershik).
    Lett. Math. Phys. 105, No. 1, 11-25
    [ abstract ] [Full text: .pdf]

  • Infinite-dimensional Schur-Weyl duality and the Coxeter-Laplace operator (with A.M.Vershik).
    Comm. Math. Phys. 327, No. 3, 873-885 (2014).
    [ abstract ] [Full text: .pdf]

  • On the behavior of the periodic Coxeter Laplacian in some representations related to the antiferromagnetic asymptotic mode and continual limits.
    Zapiski Nauchn. Semin. POMI, 390 (2011), 286-298.
    [Full text: .pdf]

  • Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case.
    Zapiski Nauchn. Semin. POMI, 378 (2010), 111-132.
    [ abstract ] [ Full text: .pdf]

  • Induced representations of the infinite symmetric group (with A.M.Vershik).
    Pure Appl. Math. Quart., 3, No. 4 (2007), 1005-1026.
    [ abstract ] [ Full text: .pdf (278 Kb) ]

  • Induced representations of the infinite symmetric group and their spectral theory (with A.M.Vershik).
    Dokl. Akad. Nauk 412, No. 1 (2007), 7-10.
    English translation: Doklady Mathematics, 75, No. 1 (2007), 1-4.
    [ abstract ] [ Full text in Russian: .pdf (84 Kb) ] [ Full text in English: .pdf (186 Kb) ]

  • Markov measures on Young tableaux and induced representations of the infinite symmetric group (with A.M.Vershik).
    Teor. Veroyatn. Primen., 51, No. 1 (2006), 47-63.
    English translation: Prob. Theory Appl., 51, No. 1 (2006), 211-223.
    [ abstract ] [ Full text in English: .ps.gz (173 Kb) ]

  • On different models of representations of the infinite symmetric group (with A.M.Vershik).
    Adv. Appl. Math., 37, 526-540 (2006).
    [ abstract ] [ Full text: .pdf (282 Kb) ]

  • Quantum inverse scattering method for the q-boson model and symmetric functions.
    Funktsional. Anal. i Prilozhen., 40, No. 3 (2006), 53-65.
    English translation: Funct. Anal. Appl., 40, No. 3 (2006), 207-217.
    [ abstract ] [ Full text in English: .pdf (201 Kb) ]

  • On the Fourier transform on the infinite symmetric group (with A.M.Vershik).
    Zapiski Nauchn. Semin. POMI, 325 (2005), 61-82.
    English translation: J. Math. Sci. (N.Y.), 138, No. 3 (2006), 5663-5673.
    [abstract ] [ Full text in English: .pdf (620Kb) ]

  • Fock factorizations, and decompositions of the L^2 spaces over general Levy processes (with A.M.Vershik).
    Uspekhi Mat. Nauk, 58, No. 3 (2003), 3-50.
    English translation: Russian Math. Surveys, 58, No. 3 (2003), 427-472.
    [abstract ] [ Full text in English: .pdf (365Kb) ]

  • Remarks on the Markov-Krein identity and quasi-invariance of the gamma process (with A.M.Vershik and M.Yor)
    Zapiski Nauchn. Semin. POMI, 283 (2001), 21-36.
    English translation: J. Math. Sci. (N.Y.), 121, No. 3 (2004), 2303-2310.
    [ abstract ] [ Full text in Russian: .ps.gz ] [ Full text in English: .pdf (160Kb) ]

  • On the simplest split-merge operator on the infinite-dimensional simplex
    PDMI preprint 03/2001, Steklov Institute of Mathematics at St.Petersburg, 2001.
    [ abstract ] [ Full text: .ps.gz (81 Kb) ]

  • An infinite-dimensional analogue of the Lebesgue measure and distinguished properties of the gamma process (with A.M.Vershik and M.Yor)
    J. Funct. Anal., 185, No. 1 (2001), 274-296.
    [ abstract ] [ Full text: .ps.gz (104 Kb) ]

  • Quasi-invariance of the gamma process and multiplicative properties of the Poisson-Dirichlet measures (with A.M.Vershik )
    C. R. Acad. Sci. Paris, 329, Serie I (1999), 163-168.
    [ abstract ] [ Full text: .ps.gz (70 Kb) ]

  • Stationary random partitions of positive integers
    Teor. Veroyatnost. i Primenen., 44, No. 1 (1999), 55-73.
    English translation: Prob. Theory Appl., 44, No. 1 (2000), 60-74.
    [ abstract ] [ Full text : .ps.gz (196 Kb) ]

  • The Markov-Krein correspondence in several dimensions (with S.V.Kerov)
    Zapiski Nauchn. Semin. POMI, 283 (2001), 98-122.
    (PDMI preprint 1/1998, Steklov Institute of Mathematics of St.Petersburg, 1998.)
    English translation: J. Math. Sci. (N.Y.) 121, No. 3 (2004), 2345-2359.
    [ abstract] [ Full text in Russian: .ps.gz (75 Kb)] [ Full text in English: .pdf (250 Kb)]

  • Distribution of mean values for some random measures
    Zapiski Nauchn. Semin. POMI, 240 (1997), 268-279.
    English translation: J. Math. Sci. (N.Y.), 96, No. 5 (1999), 3616-3623.
    [ abstract ] [ Full text in Russian: .ps.gz (77 Kb) ] [ Full text in English: .pdf (522 Kb) ]

  • Stick breaking process generates virtual permutations with Ewens distribution (with S.V.Kerov)
    Zapiski Nauchn. Semin. POMI, 223 (1995), 162-180.
    English translation: J. Math. Sci. (N.Y.), 87, No. 6 (1997), 4082-4093.
    [ abstract ]

  • Distribution of cycle lengths of infinite permutations
    Zapiski Nauchn. Semin. POMI, 232 (1995), 148-161.
    English translation: J. Math. Sci. (N.Y.), 87, No. 6 (1997), 4072-4081.
    [ abstract ]


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