  We study a distinguished random walk on affine buildings of type Ar , which
was already considered by Cartwright, Saloff-Coste and Woess. In rank r=2, it
is the simple random walk and we obtain optimal global bounds for its
transition density (same upper and lower bound, up to multiplicative
constants). In the higher rank case, we obtain sharp uniform bounds in fairly
large space-time regions which are sufficient for most applications.
