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

Sharp estimates for distinguished random walks on affine buildings of type Ar