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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 1, Pages 21–32 (Mi izv416)  

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

Group representation of the Cayley forest and some of its applications

N. N. Ganikhodzhaev, U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: Cayley forests and products of Cayley trees of order $k\geqslant 1$ are represented as subgroups in the free product of $m$ cyclic groups ($m>k$) of order 2. The automorphism groups of these objects are determined. We give a complete description of the sets of translation-invariant and periodic Gibbs measures for the Ising model on a Cayley forest. We construct a new class of limiting Gibbs measures for the inhomogeneous Ising model on a Cayley tree. We find sufficient conditions for random walks in periodic random media on the forest to be never returning provided that the jumps of the walking particle are bounded.

DOI: https://doi.org/10.4213/im416

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English version:
Izvestiya: Mathematics, 2003, 67:1, 17–27

Bibliographic databases:

UDC: 517.98+530.1
MSC: 82B20, 20E08
Received: 27.06.2001

Citation: N. N. Ganikhodzhaev, U. A. Rozikov, “Group representation of the Cayley forest and some of its applications”, Izv. RAN. Ser. Mat., 67:1 (2003), 21–32; Izv. Math., 67:1 (2003), 17–27

Citation in format AMSBIB
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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. É. P. Normatov, U. A. Rozikov, “A description of harmonic functions via properties of the group representation of the Cayley tree”, Math. Notes, 79:3 (2006), 399–407  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. M. M. Rahmatullaev, “On weakly periodic Gibbs measures of the Potts model with a special external field on a Cayley tree”, Zhurn. matem. fiz., anal., geom., 12:4 (2016), 302–314  mathnet  crossref  mathscinet
    3. Rakhmatullaev M.M., “On Weakly Periodic Gibbs Measures for the Potts Model with External Field on the Cayley Tree”, Ukr. Math. J., 68:4 (2016), 598–611  crossref  mathscinet  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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