Loading [MathJax]/jax/output/SVG/config.js
Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Matematicheskie Zametki, 2002, Volume 72, Issue 4, Pages 516–527
DOI: https://doi.org/10.4213/mzm441 (Mi mzm441) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Representability of Trees and Some of Their Applications

U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
Full-text PDF (225 kB) Citations (6)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm441
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.
Received: 30.11.2000
Revised: 05.02.2002
English version:
Mathematical Notes, 2002, Volume 72, Issue 4, Pages 479–488
DOI: https://doi.org/10.1023/A:1020580227830
Bibliographic databases:
UDC: 519.17+530.1
Language: Russian
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
\Bibitem{Roz02}
\by U.~A.~Rozikov
\paper Representability of Trees and Some of Their Applications
\jour Mat. Zametki
\yr 2002
\vol 72
\issue 4
\pages 516--527
\mathnet{http://mi.mathnet.ru/mzm441}
\crossref{https://doi.org/10.4213/mzm441}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1963147}
\zmath{https://zbmath.org/?q=an:1028.82008}
\transl
\jour Math. Notes
\yr 2002
\vol 72
\issue 4
\pages 479--488
\crossref{https://doi.org/10.1023/A:1020580227830}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000179160400022}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0141848649}
Linking options:
  • https://www.mathnet.ru/eng/mzm441
  • https://doi.org/10.4213/mzm441
  • https://www.mathnet.ru/eng/mzm/v72/i4/p516
    • This publication is cited in the following 6 articles:
    1. Ny A.L., Liao L., Rozikov U.A., “P-Adic Boundary Laws and Markov Chains on Trees”, Lett. Math. Phys., 110:10 (2020), 2725–2741  crossref  mathscinet  isi  scopus
    2. 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
    3. O. N. Khakimov, “On a generalized p-adic Gibbs measure for Ising model on trees”, P-Adic Num Ultrametr Anal Appl, 6:3 (2014), 207  crossref
    4. 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
    5. [Anonymous], “A Multi-Dimensional-Time Dynamical System”, Qual. Theor. Dyn. Syst., 12:2 (2013), 361–375  crossref  mathscinet  isi  scopus  scopus
    6. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:376
    Full-text PDF :176
    References:85
    First page:1
     
      Contact us:
    math-net2025_05@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025