In this talk, I will discuss the continuity and regularity of escape rate of random walks on CAT(0) spaces with a rank-1 isometry. I will then explain the analyticity of escape rate on some CAT(0) cube complices and Teichmüller space, These are re-discoveries and generalizations of the earlier results of Erschler-Kaimanovich, Gouëzel, Ledrappier and Mathieu. Our approach is based on a new boundary-free approach due to Gouëzel. Time permitting, I will explain the continuity of asymptotic entropy that is independently due to Erschler and Frisch.