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Mat. Zametki, 2002, Volume 72, Issue 4, Pages 516–527 (Mi mz441)  

This article is cited in 4 scientific papers (total in 4 papers)

Representability of Trees and Some of Their Applications

U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We prove that if a tree is representable as the free product of a finite set of cyclic groups of order two, then it is necessarily a Caley tree. For other trees, their presentations as some finite sets of sequences constructed from some recurrence relations are described. Using these presentations, we give a complete description of translation-invariant measures and a class of periodic Gibbs measures for a nonhomogeneous Ising model on an arbitrary tree. A sufficient condition for a random walk in a random environment on an arbitrary tree to be transient is described.

DOI: https://doi.org/10.4213/mzm441

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English version:
Mathematical Notes, 2002, 72:4, 479–488

Bibliographic databases:

UDC: 519.17+530.1
Received: 30.11.2000
Revised: 05.02.2002

Citation: U. A. Rozikov, “Representability of Trees and Some of Their Applications”, Mat. Zametki, 72:4 (2002), 516–527; Math. Notes, 72:4 (2002), 479–488

Citation in format AMSBIB
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\paper Representability of Trees and Some of Their Applications
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\issue 4
\pages 516--527
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\vol 72
\issue 4
\pages 479--488
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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. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus  scopus
    3. [Anonymous], “A Multi-Dimensional-Time Dynamical System”, Qual. Theor. Dyn. Syst., 12:2 (2013), 361–375  crossref  mathscinet  isi  scopus  scopus
    4. Ahmad Mohd Ali Khameini, Liao L., Saburov M., “Periodic P-Adic Gibbs Measures of Q-State Potts Model on Cayley Trees i: the Chaos Implies the Vastness of the Set of P-Adic Gibbs Measures”, J. Stat. Phys., 171:6 (2018), 1000–1034  crossref  mathscinet  zmath  isi  scopus  scopus
  • Математические заметки Mathematical Notes
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