[Sur les graphes d'allumeur de réverbères, les fonctions harmoniques de p-énergie finie sont constantes]
The aim of this note is to show that lamplighter graphs where the space graph is infinite and at most two-ended and the lamp graph is at most two-ended do not admit harmonic functions with gradients in
Le but de cette note est de montrer que plusieurs graphes d'allumeurs de réverbères, où le graphe d'espace est infini avec au plus deux bouts et le graphe des lampes a au plus deux bouts, ne possèdent pas de fonction harmonique non constante à gradient
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Antoine Gournay 1
@article{CRMATH_2016__354_8_762_0, author = {Antoine Gournay}, title = {Harmonic functions with finite \protect\emph{p}-energy on lamplighter graphs are constant}, journal = {Comptes Rendus. Math\'ematique}, pages = {762--765}, publisher = {Elsevier}, volume = {354}, number = {8}, year = {2016}, doi = {10.1016/j.crma.2016.04.015}, language = {en}, }
Antoine Gournay. Harmonic functions with finite p-energy on lamplighter graphs are constant. Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 762-765. doi : 10.1016/j.crma.2016.04.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.04.015/
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