122 citations · 308 across the 18 of their papers we have counts for
18 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…
On a recursive construction of Dirichlet form on the Sierpiński gasket
Qingsong Gu, Ka-Sing Lau, Hua Qiu
Let denote the -th level Sierpiński graph of the Sierpiński gasket . We consider, for any given conductance on , the Dirchlet form …
Dirichlet forms and critical exponents on fractals
Qingsong Gu, Ka-Sing Lau
Let denote the Besov space defined on a compact set which is equipped with an -regular measure . The {\it critical exponent} is…
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…
On Hyperbolic graphs induced by iterated function systems
Ka-Sing Lau, Xiang-Yang Wang
For any contractive iterated function system (IFS, including the Moran systems), we show that there is a natural hyperbolic graph on the symbolic space, which yields the Hölder equ…