Heat kernel and Green function estimates on affine buildings of type   $\tilde{A}_r$
  We 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. 
Jean-Philippe Anker (MAPMO), Bruno Schapira (MAPMO, PMA), Bartosz   Trojan (MAPMO)