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Zap. Nauchn. Sem. POMI, 2012, Volume 403, Pages 5–18 (Mi znsl5245)  

This article is cited in 2 scientific papers (total in 2 papers)

Multiple-grain dissipative sandpiles

N. M. Bogoliubova, A. G. Pronkoa, J. Timonenb

a St. Petersburg Department of V. A. Steklov Institute of Mathematics, St. Petersburg, Russia
b Department of Physics, University of Jyväskylä, Jyväskylä, Finland

Abstract: The two-dimensional directed sandpile with dissipation is transformed into a $(1+1)$-dimensional problem with discrete space and continuous “time”. The master equation for the conditional probability that $K$ grains preserve their initial order during an avalanche is solved exactly. Explicit expressions for asymptotic forms of solutions are given for the cases of the infinite and semi-infinite lattices. A nontrivial scaling is found in both cases.

Key words and phrases: dissipative sandpiles, master equations, multi-grain correlations, conditional probabilities.

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English version:
Journal of Mathematical Sciences (New York), 2013, 190:3, 411–418

Bibliographic databases:

UDC: 519.248.25
Received: 03.10.2012
Language:

Citation: N. M. Bogoliubov, A. G. Pronko, J. Timonen, “Multiple-grain dissipative sandpiles”, Representation theory, dynamical systems, combinatorial methods. Part XXI, Zap. Nauchn. Sem. POMI, 403, POMI, St. Petersburg, 2012, 5–18; J. Math. Sci. (N. Y.), 190:3 (2013), 411–418

Citation in format AMSBIB
\Bibitem{BogProTim12}
\by N.~M.~Bogoliubov, A.~G.~Pronko, J.~Timonen
\paper Multiple-grain dissipative sandpiles
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXI
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 403
\pages 5--18
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5245}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3029577}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 190
\issue 3
\pages 411--418
\crossref{https://doi.org/10.1007/s10958-013-1256-2}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880600999}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Perez-Garcia D. Tierz M., “Chern–Simons Theory Encoded on a Spin Chain”, J. Stat. Mech.-Theory Exp., 2016, 013103  crossref  mathscinet  isi  scopus
    2. J. Math. Sci. (N. Y.), 238:6 (2019), 769–778  mathnet  crossref
  • Записки научных семинаров ПОМИ
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