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Zap. Nauchn. Sem. POMI, 1995, Volume 223, Pages 162–180 (Mi znsl4386)  

This article is cited in 3 scientific papers (total in 4 papers)

Combinatorial and algorithmic methods

Stick breaking process generated by virtual permutations with Ewens distribution

S. V. Kerova, N. V. Tsilevichb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
b Saint-Petersburg State University

Abstract: Given a sequence $x$ of points in the unit interval, we associate with it a virtual permutation $w=w(x)$ (that is, a sequence $w$ of permutations $w_n\in\mathfrak S_n$ such that for all $n=1,2,…$, $w_{n-1}=w'_n$ is obtained from $w_n$ by removing the last element $n$ from its cycle). We introduce a detailed version of the well-known stick breaking process generating a random sequence $x$. It is proved that the associated random virtual permutation $w(x)$ has a Ewens distribution. Up to subsets of zero measure, the space $\mathfrak S_n=\varprojlim\mathfrak S_n$ of virtual permutations is identified with the cube $[0,1]^\infty$. Bibliography: 8 titles.

Full text: PDF file (865 kB)

English version:
Journal of Mathematical Sciences (New York), 1997, 87:6, 4082–4093

Bibliographic databases:

UDC: 519.217+517.986
Received: 15.04.1995

Citation: S. V. Kerov, N. V. Tsilevich, “Stick breaking process generated by virtual permutations with Ewens distribution”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part I, Zap. Nauchn. Sem. POMI, 223, POMI, St. Petersburg, 1995, 162–180; J. Math. Sci. (New York), 87:6 (1997), 4082–4093

Citation in format AMSBIB
\Bibitem{KerTsi95}
\by S.~V.~Kerov, N.~V.~Tsilevich
\paper Stick breaking process generated by virtual permutations with Ewens distribution
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~I
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 223
\pages 162--180
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4386}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1374319}
\zmath{https://zbmath.org/?q=an:0909.60018|0887.60016}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 87
\issue 6
\pages 4082--4093
\crossref{https://doi.org/10.1007/BF02355804}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Olshanski C., “An introduction to harmonic analysis on the infinite symmetric group”, Asymptotic Combinatorics with Applications to Mathematical Physics, Lecture Notes in Mathematics, 1815, 2003, 127–160  crossref  zmath  isi
    2. J. Math. Sci. (N. Y.), 138:3 (2006), 5699–5710  mathnet  crossref  mathscinet  zmath
    3. Griffiths R.C. Spano D., “Record Indices and Age-Ordered Frequencies in Exchangeable Gibbs Partitions”, Electron. J. Probab., 12 (2007), 40, 1101–1130  crossref  zmath  isi
    4. A. M. Borodin, Aleksandr I. Bufetov, Aleksei I. Bufetov, A. M. Vershik, V. E. Gorin, A. I. Molev, V. F. Molchanov, R. S. Ismagilov, A. A. Kirillov, M. L. Nazarov, Yu. A. Neretin, N. I. Nessonov, A. Yu. Okounkov, L. A. Petrov, S. M. Khoroshkin, “Grigori Iosifovich Olshanski (on his 70th birthday)”, Russian Math. Surveys, 74:3 (2019), 555–577  mathnet  crossref  crossref  adsnasa  isi  elib
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