On a Class of Markov Semigroups on Discrete Ultra-Metric Spaces Auteur(s): Bendikov Alexander, Grigor’yan Alexander, Pittet Christophe (Article) Publié: Potential Analysis, vol. 37 p.125-169 (2012) Ref HAL: hal-01305034_v1 DOI: 10.1007/s11118-011-9249-6 Exporter : BibTex | endNote Résumé: We consider a discrete ultra-metric space $\left( X,d\right)$ with a measure m and construct in a natural way a symmetric Markov semigroup $\left\{ P_{t}\right\} _{t\geq 0}$ in $L^{2}\left( X,m\right)$ and the corresponding Markov process $\left\{ \mathcal{X}_{t}\right\}$ . We prove upper and lower bounds of its transition function and its Green function, give a criterion for the transience, and estimate its moments.