On the displacement function of isometries of Euclidean buildings
  In this note we study the displacement function $d_g(x):=d(gx,x)$ of an isometry $g$ of a Euclidean building. We give a lower bound for $d_g(x)$ depending on the distance from $x$ to the minimal set of $g$. 
Carlos Ramos-Cuevas
math.MG