18 citations · 29 across the 4 of their papers we have counts for
4 papers
Gromov Hyperbolic Graphs Arising From Iterations
Shi-Lei Kong, Ka-Sing Lau, Xiang-Yang Wang
For a contractive iterated function system (IFS), it is known that there is a natural hyperbolic graph structure (augmented tree) on the symbolic space of the IFS that reflects the…
Random walks and induced Dirichlet forms on compact spaces of homogeneous type
Shi-Lei Kong, Ka-Sing Lau, Ting-Kam Leonard Wong
We extend our study of random walks and induced Dirichlet forms on self-similar sets [arXiv:1604.05440, 1612.01708] to compact spaces of homogeneous type . A successive p…
Critical exponents of induced Dirichlet forms on self-similar sets
Shi-Lei Kong, Ka-Sing Lau
In a previous paper [arXiv:1604.05440], we studied certain random walks on the hyperbolic graphs associated with the self-similar sets , and showed that the discrete energy…
Random walks and induced Dirichlet forms on self-similar sets
Shi-Lei Kong, Ka-Sing Lau, Ting-Kam Leonard Wong
Let be a self-similar set satisfying the open set condition. Following Kaimanovich's elegant idea, it has been proved that on the symbolic space of a natural augmented…