Tsilevich, Natalia Vladimirovna

Statistics Math-Net.Ru
Total publications: 15
Scientific articles: 14
Presentations: 5

Number of views:
This page:1547
Abstract pages:3927
Full texts:1131
Candidate of physico-mathematical sciences (1998)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Keywords: representation theory; asymptotic combinatorics; Poisson–Dirichlet measures; random processes.


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.


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.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. A. M. Vershik, N. V. Tsilevich, “On the Relationship between Combinatorial Functions and Representation Theory”, Funktsional. Anal. i Prilozhen., 51:1 (2017),  28–39  mathnet  mathscinet  elib; Funct. Anal. Appl., 51:1 (2017), 22–31  isi  scopus
2. N. V. Tsilevich, “On the dual complexity and spectra of some combinatorial functions”, Zap. Nauchn. Sem. POMI, 462 (2017),  112–121  mathnet; J. Math. Sci. (N. Y.), 232:2 (2018), 170–176  scopus
3. 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  mathnet; J. Math. Sci. (N. Y.), 181:6 (2012), 914–920  scopus
4. N. V. Tsilevich, “Spectral properties of the periodic Coxeter Laplacian in the two-row ferromagnetic case”, Zap. Nauchn. Sem. POMI, 378 (2010),  111–132  mathnet; J. Math. Sci. (N. Y.), 174:1 (2011), 58–70  scopus
5. , 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  mathnet  mathscinet
6. N. V. Tsilevich, “Quantum Inverse Scattering Method for the $q$-Boson Model and Symmetric Functions”, Funktsional. Anal. i Prilozhen., 40:3 (2006),  53–65  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 40:3 (2006), 207–217  isi  scopus
7. 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  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 51:1 (2007), 211–223  isi  elib  scopus
8. A. M. Vershik, N. V. Tsilevich, “On the Fourier transform on the infinite symmetric group”, Zap. Nauchn. Sem. POMI, 325 (2005),  61–82  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 138:3 (2006), 5663–5673  scopus
9. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 58:3 (2003), 427–472  isi  scopus
10. S. V. Kerov, N. V. Tsilevich, “The Markov–Krein correspondence in several dimensions”, Zap. Nauchn. Sem. POMI, 283 (2001),  98–122  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 121:3 (2004), 2345–2359
11. 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  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 121:3 (2004), 2303–2310
12. N. V. Tsilevich, “Stationary random partitions of positive integers”, Teor. Veroyatnost. i Primenen., 44:1 (1999),  55–73  mathnet  mathscinet  zmath; Theory Probab. Appl., 44:1 (2000), 60–74  isi
13. N. V. Tsilevich, “Distributions of the mean values for some random measures”, Zap. Nauchn. Sem. POMI, 240 (1997),  268–279  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 96:5 (1999), 3616–3623
14. S. V. Kerov, N. V. Tsilevich, “Stick breaking process generated by virtual permutations with Ewens distribution”, Zap. Nauchn. Sem. POMI, 223 (1995),  162–180  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 87:6 (1997), 4082–4093
15. N. V. Tsilevich, “Distribution of cycle lengths of infinite permutations”, Zap. Nauchn. Sem. POMI, 223 (1995),  148–161  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 87:6 (1997), 4072–4081

16. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 69:1 (2014), 165–179  isi

Presentations in Math-Net.Ru
1. Распределения Пуассона-Дирихле
N. V. Tsilevich
Seminar of Chebyshev Laboratory on Probability Theory
March 5, 2015 13:00
2. Infinite-dimensional Schur-Weyl duality and the Coxeter-Laplace operator
N. V. Tsilevich
St. Petersburg Seminar on Representation Theory and Dynamical Systems
September 19, 2012 17:00
3. Schur processes and random Young diagrams (completion)
N. V. Tsilevich
Seminar on Stochastics
March 18, 2011 15:30
4. Schur processes and random Young diagrams
N. V. Tsilevich
Seminar on Stochastics
March 11, 2011 15:30
5. Infinite-dimensional analogue of the Lebesgue measure and some properties of the gamma process
N. V. Tsilevich
Meetings of the St. Petersburg Mathematical Society
November 21, 2000

Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019