Geodesic
Representability of Trees and Some of Their Applications
Matematičeskie zametki, Tome 72 (2002) no. 4, pp. 516-527

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2002_72_4_a4,
     author = {U. A. Rozikov},
     title = {Representability of {Trees} and {Some} of {Their} {Applications}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {516--527},
     publisher = {mathdoc},
     volume = {72},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a4/}
}
TY  - JOUR
AU  - U. A. Rozikov
TI  - Representability of Trees and Some of Their Applications
JO  - Matematičeskie zametki
PY  - 2002
SP  - 516
EP  - 527
VL  - 72
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a4/
LA  - ru
ID  - MZM_2002_72_4_a4
ER  - 
%0 Journal Article
%A U. A. Rozikov
%T Representability of Trees and Some of Their Applications
%J Matematičeskie zametki
%D 2002
%P 516-527
%V 72
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a4/
%G ru
%F MZM_2002_72_4_a4
U. A. Rozikov. Representability of Trees and Some of Their Applications. Matematičeskie zametki, Tome 72 (2002) no. 4, pp. 516-527. http://geodesic.mathdoc.fr/item/MZM_2002_72_4_a4/