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Zap. Nauchn. Sem. POMI, 2016, Volume 448, Pages 48–68 (Mi znsl6302)  

This article is cited in 1 scientific paper (total in 1 paper)

Multi-dimensional random walks and integrable phase models

N. Bogoliubovab, C. Malyshevab

a St. Petersburg Department of Steklov Institute of Mathematics, Fontanka 27, St. Petersburg, Russia
b ITMO University, Kronverksky 49, St. Petersburg, Russia

Abstract: We consider random multi-dimensional lattice walks bounded by a hyperplane, calling them walks over multi-dimensional simplicial lattices. We demonstrate that generating functions of these walks are dynamical correlation functions of a certain type of exactly solvable quantum phase models describing strongly correlated bosons on a chain. Walks over oriented lattices are related to the phase model with a non-Hermitian Hamiltonian, while walks over disoriented ones are related to the model with a Hermitian Hamiltonian. The calculation of the generating functions is based on the algebraic Bethe Ansatz approach to the solution of integrable models. The answers are expressed through symmetric functions. Continuous-time quantum walks bounded by a one-dimensional lattice of finite length are also studied.

Key words and phrases: multi-dimensional random walk, quantum walk, phase model, correlation function, symmetric functions.

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English version:
Journal of Mathematical Sciences (New York), 2017, 224:2, 199–213

Bibliographic databases:

UDC: 517.9+519.248.25
Received: 06.10.2016
Language:

Citation: N. Bogoliubov, C. Malyshev, “Multi-dimensional random walks and integrable phase models”, Representation theory, dynamical systems, combinatorial methods. Part XXVII, Zap. Nauchn. Sem. POMI, 448, POMI, St. Petersburg, 2016, 48–68; J. Math. Sci. (N. Y.), 224:2 (2017), 199–213

Citation in format AMSBIB
\Bibitem{BogMal16}
\by N.~Bogoliubov, C.~Malyshev
\paper Multi-dimensional random walks and integrable phase models
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXVII
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 448
\pages 48--68
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6302}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3576248}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 224
\issue 2
\pages 199--213
\crossref{https://doi.org/10.1007/s10958-017-3405-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019707450}


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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. N. Bogoliubov, C. Malyshev, “Correlation functions as nests of self-avoiding paths”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 24, Zap. nauchn. sem. POMI, 465, POMI, SPb., 2017, 27–45  mathnet
  • Записки научных семинаров ПОМИ
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