2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119915We obtain a global estimate of the transition density $p^n(0,x)$ associated to a nearest neighbor random walk, called here "simple", on affine buildings of type $\widetilde{A}_r$. Then we deduce a global estimate of the Green function. This is the analogue of a result on Riemannian symmetric spaces of the noncompact type.Classical Analysis and ODEsProbabilityPrimary: 42C05; 51E24; 60B15; 60J10. Secondary: 31C12; 31C35; 33C52; 33E50; 60J45; 60J50text