75 citations · 327 across the 49 of their papers we have counts for
50 papers
Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces
Takashi Kumagai, Nageswari Shanmugalingam, Ryosuke Shimizu
In the context of a metric measure space , we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of th…
On Kigami's conjecture of the embedding
Shiping Cao, Zhen-Qing Chen, Takashi Kumagai
Let be a connected compact metric space and . Under the assumption of \cite[Assumption 2.15]{Ki2} and the conductive -homogeneity, we show that $\mathc…
Quantitative stochastic homogenization for random conductance models with stable-like jumps
Xin Chen, Zhen-Qing Chen, Takashi Kumagai +1
We consider random conductance models with long range jumps on , where the one-step transition probability from to is proportional to with $α\in…
Limit theorems for some long range random walks on torsion free nilpotent groups
Zhen-Qing Chen, Takashi Kumagai, Laurent Saloff-Coste +2
We consider a natural class of long range random walks on torsion free nilpotent groups and develop limit theorems for these walks. Given the original discrete group and a rand…
Spectral dimension of simple random walk on a long-range percolation cluster
Van Hao Can, David A. Croydon, Takashi Kumagai
Consider the long-range percolation model on the integer lattice in which all nearest-neighbour edges are present and otherwise and are connected with probab…
Heat kernels for reflected diffusions with jumps on inner uniform domains
Zhen-Qing Chen, Panki Kim, Takashi Kumagai +1
In this paper, we study sharp two-sided heat kernel estimates for a large class of symmetric reflected diffusions with jumps on the closure of an inner uniform domain in a leng…