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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 335, Pages 59–74 (Mi znsl209)  
This article is cited in 17 scientific papers (total in 17 papers)

Integrable models for the vicious and friendly walkers

N. M. Bogolyubov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (261 kB) Citations (17)
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Abstract: Random walks of the essentially different classes of random walkers, namely of the vicious and of the friendly ones, on the one-dimensional lattices with the periodic boundary conditions are considered. The walkers are called vicious since arriving on the same lattice site they annihilate not only one another but all the rest as well. On the contrary, the arbitrary number of the friendly walkers can share the same lattice sites. It is shown that the natural model describing the behavior of the friendly walkers is the integrable model of the boson type. The representation of the generating function for the number of the lattice paths made by the fixed number of the friendly walkers for the certain number of steps is obtained.
Received: 02.06.2006
English version:
Journal of Mathematical Sciences (New York), 2007, Volume 143, Issue 1, Pages 2729–2737
DOI: https://doi.org/10.1007/s10958-007-0160-z
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: N. M. Bogolyubov, “Integrable models for the vicious and friendly walkers”, Questions of quantum field theory and statistical physics. Part 19, Zap. Nauchn. Sem. POMI, 335, POMI, St. Petersburg, 2006, 59–74; J. Math. Sci. (N. Y.), 143:1 (2007), 2729–2737
Citation in format AMSBIB
\Bibitem{Bog06}
\by N.~M.~Bogolyubov
\paper Integrable models for the vicious and friendly walkers
\inbook Questions of quantum field theory and statistical physics. Part~19
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 335
\pages 59--74
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl209}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2269751}
\zmath{https://zbmath.org/?q=an:1127.82023}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 1
\pages 2729--2737
\crossref{https://doi.org/10.1007/s10958-007-0160-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247394520}
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  • https://www.mathnet.ru/eng/znsl/v335/p59
    • This publication is cited in the following 17 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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