This article is cited 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

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.

UDC: 519.17+530.1

Received: 30.11.2000
Revised: 05.02.2002

DOI: 10.4213/mzm441

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

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