Affine buildings are non-Archimedean analogous of Riemannian symmetric spaces. They were invented by F. Bruhat and J. Tits to study semisimple algebraic groups over non-Archimedean local fields, e.g. $SL(n, Q_p)$ where $Q_p$ denote $p$-adic numbers. For example affine buildings corresponding to real hyperbolic spaces are semihomogeneous trees. However, there are low rank buildings with small group of automorphisms. For this reason we take purely geometric approach to compactifications. In the talk after brief introduction to affine buildings we discuss some classical compactification procedures (i.e. Gromov, Caprace-Lecureux, Furstenberg). In the second part we describe Martin compactifications corresponding to certain class of random walks which is our main result.

joint work with Bertrand Rémy