科研讨论班

Self-affine measures naturally arise as stationary measures of random walks driven by affine contractions on Euclidean spaces. In this talk, we study conditions under which their dimensions attain the symbolic upper bound. We establish verifiable and mild criteria in the diagonal case. In discussing the proof, we highlight the role of additive combinatorics, the challenges posed by non-homogeneous systems in higher dimensions, and the product structure for the local dimension of certain random measures.