representation theory; asymptotic combinatorics; Poisson–Dirichlet measures; random processes.
Subject:
Formulas for distributions of mean values of linear functionals with respect to generalized Dirichlet processes, as well as for joint distributions of mean values of several linear functionals with respect to Dirichlet processes are obtained. In a joint work with S. V. Kerov a multidimensional Markov–Krein transform is introduced and studied. New characterizations of the Poisson–Dirichlet measures are obtained. In a series of papers (joint with A. Vershik and M. Yor) invariance properties of gamma processes are used to introduce and study a family of so called multiplicative measures, including an infinite-dimensional analogue of the Lebesgue measure. The developed theory is applied to studying Poisson–Dirichlet measures, stable processes, Markov–Krein identity and to the representation theory of current groups.
Biography
Graduated from St. Petersburg State University in 1995. PhD — 1998, Steklov Institute of Mathematics at St. Petersburg. About 10 scientific publications. A member of St. Petersburg Mathematical Society since 1999.
Young Mathematician Prize of St. Petersburg Mathematical Society for a series of papers on the Poisson–Dirichlet measures, 1999.
Main publications:
N. Tsilevich, A. Vershik, M. Yor. An infinite-dimensional analogue of the Lebesgue measure, and distinguished properties of the gamma process // J. Funct. Anal., v. 185, no. 1, 274–296, 2001.
N. Tsilevich, A. Vershik. Quasi-invariance of the gamma process and multiplicative properties of the Poisson–Dirichlet measures // C. R. Acad. Sci. Paris, v. 329, Ser. I, p. 163–168, 1999.
A. M. Vershik, N. V. Tsilevich, “The Schur–Weyl graph and Thoma's theorem.”, Funktsional. Anal. i Prilozhen., 55:3 (2021), 26–41; Funct. Anal. Appl., 55:3 (2021), 198–209
A. M. Vershik, N. V. Tsilevich, “Ergodicity and Totality of Partitions Associated with the RSK Correspondence”, Funktsional. Anal. i Prilozhen., 55:1 (2021), 33–42; Funct. Anal. Appl., 55:1 (2021), 26–33
A. M. Vershik, N. V. Tsilevich, “Groups generated by involutions of diamond-shaped graphs, and deformations of Young's orthogonal form”, Zap. Nauchn. Sem. POMI, 481 (2019), 29–38
A. M. Vershik, N. V. Tsilevich, “On the Relationship between Combinatorial Functions and Representation Theory”, Funktsional. Anal. i Prilozhen., 51:1 (2017), 28–39; Funct. Anal. Appl., 51:1 (2017), 22–31
N. V. Tsilevich, “On the dual complexity and spectra of some combinatorial functions”, Zap. Nauchn. Sem. POMI, 462 (2017), 112–121; J. Math. Sci. (N. Y.), 232:2 (2018), 170–176
N. V. Tsilevich, “On the behavior of the periodic Coxeter Laplacian in some representations related to the antiferromagnetic asymptotic mode and continual limits”, Zap. Nauchn. Sem. POMI, 390 (2011), 286–298; J. Math. Sci. (N. Y.), 181:6 (2012), 914–920
N. V. Tsilevich, “Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case”, Zap. Nauchn. Sem. POMI, 378 (2010), 111–132; J. Math. Sci. (N. Y.), 174:1 (2011), 58–70
, A. M. Vershik, N. V. Tsilevich, “Induced representations of the infinite symmetric group and their
spectral theory”, Dokl. Akad. Nauk, 412:1 (2007), 7–10
N. V. Tsilevich, “Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 53–65; Funct. Anal. Appl., 40:3 (2006), 207–217
A. M. Vershik, N. V. Tsilevich, “Markov measures on Young tableaux and induced representations of an infinite symmetric group”, Teor. Veroyatnost. i Primenen., 51:1 (2006), 47–63; Theory Probab. Appl., 51:1 (2007), 211–223
A. M. Vershik, N. V. Tsilevich, “On the Fourier transform on the infinite symmetric group”, Zap. Nauchn. Sem. POMI, 325 (2005), 61–82; J. Math. Sci. (N. Y.), 138:3 (2006), 5663–5673
A. M. Vershik, N. V. Tsilevich, “Fock factorizations, and decompositions of the $L^2$ spaces over general Lévy processes”, Uspekhi Mat. Nauk, 58:3(351) (2003), 3–50; Russian Math. Surveys, 58:3 (2003), 427–472
S. V. Kerov, N. V. Tsilevich, “The Markov–Krein correspondence in several dimensions”, Zap. Nauchn. Sem. POMI, 283 (2001), 98–122; J. Math. Sci. (N. Y.), 121:3 (2004), 2345–2359
A. M. Vershik, M. Yor, N. V. Tsilevich, “Remarks on the Markov–Krein identity and quasi-invariance of the gamma process”, Zap. Nauchn. Sem. POMI, 283 (2001), 21–36; J. Math. Sci. (N. Y.), 121:3 (2004), 2303–2310
N. V. Tsilevich, “Stationary random partitions of positive integers”, Teor. Veroyatnost. i Primenen., 44:1 (1999), 55–73; Theory Probab. Appl., 44:1 (2000), 60–74
N. V. Tsilevich, “Distributions of the mean values for some random measures”, Zap. Nauchn. Sem. POMI, 240 (1997), 268–279; J. Math. Sci. (New York), 96:5 (1999), 3616–3623
S. V. Kerov, N. V. Tsilevich, “Stick breaking process generated by virtual permutations with Ewens distribution”, Zap. Nauchn. Sem. POMI, 223 (1995), 162–180; J. Math. Sci. (New York), 87:6 (1997), 4082–4093
N. V. Tsilevich, “Distribution of cycle lengths of infinite permutations”, Zap. Nauchn. Sem. POMI, 223 (1995), 148–161; J. Math. Sci. (New York), 87:6 (1997), 4072–4081
V. M. Buchstaber, M. I. Gordin, I. A. Ibragimov, V. A. Kaimanovich, A. A. Kirillov, A. A. Lodkin, S. P. Novikov, A. Yu. Okounkov, G. I. Olshanski, F. V. Petrov, Ya. G. Sinai, L. D. Faddeev, S. V. Fomin, N. V. Tsilevich, Yu. V. Yakubovich, “Anatolii Moiseevich Vershik (on his 80th birthday)”, Uspekhi Mat. Nauk, 69:1(415) (2014), 173–186; Russian Math. Surveys, 69:1 (2014), 165–179
Presentations in Math-Net.Ru
1.
The Schur–Weyl graph and Thoma’s theorem N. V. Tsilevich New Perspectives in Asymptotic Representation Theory. In memory of Sergei Kerov (1946–2000) August 24, 2021 11:00
2.
Ðàñïðåäåëåíèÿ Ïóàññîíà-Äèðèõëå N. V. Tsilevich Seminar of Chebyshev Laboratory on Probability Theory March 5, 2015 13:00
Contact us: