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Zap. Nauchn. Sem. POMI, 2006, Volume 335, Pages 59–74 (Mi znsl209)  

This article is cited in 10 scientific papers (total in 10 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

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.

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English version:
Journal of Mathematical Sciences (New York), 2007, 143:1, 2729–2737

Bibliographic databases:

UDC: 517.9
Received: 02.06.2006

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
\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
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 143
\issue 1
\pages 2729--2737

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    This publication is cited in the following articles:
    1. N. M. Bogolyubov, “Four-vertex model”, J. Math. Sci. (N. Y.), 151:2 (2008), 2816–2828  mathnet  crossref  mathscinet
    2. J. Math. Sci. (N. Y.), 158:6 (2009), 771–786  mathnet  crossref  zmath
    3. N. M. Bogolyubov, K. L. Malyshev, “Correlation functions of the XX Heisenberg magnet and random walks of vicious walkers”, Theoret. and Math. Phys., 159:2 (2009), 563–574  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    4. Nikolay M. Bogolyubov, “Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model”, SIGMA, 5 (2009), 052, 11 pp.  mathnet  crossref  mathscinet  zmath
    5. N. M. Bogoliubov, K. Malyshev, “The correlation functions of the $XXZ$ Heisenberg chain in the case of zero or infinite anisotropy, and random walks of vicious walkers”, St. Petersburg Math. J., 22:3 (2011), 359–377  mathnet  crossref  mathscinet  zmath  isi
    6. J. Math. Sci. (N. Y.), 200:6 (2014), 662–670  mathnet  crossref
    7. N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    8. J. Math. Sci. (N. Y.), 216:1 (2016), 8–22  mathnet  crossref  mathscinet
    9. J. Math. Sci. (N. Y.), 238:6 (2019), 769–778  mathnet  crossref
    10. J. Math. Sci. (N. Y.), 242:5 (2019), 628–635  mathnet  crossref
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