6 citations · 19 across the 8 of their papers we have counts for
8 papers
Dimension theory of group actions by circle diffeomorphisms II: Minimal sets
Weikun He, Yuxiang Jiao, Disheng Xu +1
We establish a dimension theory for smooth group actions on the circle. For finitely generated groups of real-analytic circle diffeomorphisms preserving a Cantor minimal set, we in…
Semisimple random walks on the torus
Weikun He, Nicolas de Saxcé
We study linear random walks on the torus and show a quantitative equidistribution statement, under the assumption that the Zariski closure of the acting group is semisimple.
Affine random walks on the torus
Weikun He, Tsviqa Lakrec, Elon Lindenstrauss
We consider random walks on the torus arising from the action of the group of affine transformations. We give a quantitative equidistribution result for this random walk under the…
Linear random walks on the torus
Weikun He, Nicolas de Saxcé
We prove a quantitative equidistribution result for linear random walks on the torus, similar to a theorem of Bourgain, Furman, Lindenstrauss and Mozes, but without any proximality…
Random walks on linear groups satisfying a Schubert condition
Weikun He
We study random walks on whose proximal dimension is larger than and whose limit set in the Grassmannian is not…
Sum-product for real Lie groups
Weikun He, Nicolas de Saxcé
We prove a discretized sum-product theorem for representations of Lie groups whose Jordan-Hölder decomposition does not contain the trivial representation. This expansion result is…
Orthogonal projections of discretized sets
Weikun He
We generalize Bourgain's discretized projection theorem to higher rank situations. Like Bourgain's theorem, our result yields an estimate for the Hausdorff dimension of the excepti…
Discretized sum-product estimates in matrix algebras
Weikun He
We generalize Bourgain's discretized sum-product theorem to matrix algebras.