6 papers
High-order convergence rates of periodic homogenization for symmetric Lévy type operators
Xin Chen, Zhen-Qing Chen, Takashi Kumagai +1
In this paper, we establish higher-order convergence rates of the periodic homogenizatio for symmetric Lévy-type operators, encompassing the subcritical -stable regime, critic…
Quantitative homogenization on time-dependent random conductance models with stable-like jumps
Xin Chen, Zhen-Qing Chen, Takashi Kumagai +1
We establish quantitative homogenization results for time-dependent random conductance models with stable-like long range jumps on , where the transition probability from …
Gradient estimates of the heat kernel for random walks among time-dependent random conductances
Jean-Dominique Deuschel, Takashi Kumagai, Martin Slowik
In this paper we consider a time-continuous random walk in in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these ra…
Local boundedness of solutions to parabolic equations associated with fractional -Laplacian type operators
Takashi Kumagai, Jian Wang, Meng-ge Zhang
In this paper, we study the local boundedness of local weak solutions to the following parabolic equation associated with fractional -Laplacian type operators $$ \partial_t u(t,…
Quantitative periodic homogenization for symmetric non-local stable-like operators
Xin Chen, Zhen-Qing Chen, Takashi Kumagai +1
Homogenization for non-local operators in periodic environments has been studied intensively. So far, these works are mainly devoted to the qualitative results, that is, to determi…
Quenched local limit theorem for random conductance models with long-range jumps
Xin Chen, Takashi Kumagai, Jian Wang
We establish the quenched local limit theorem for reversible random walk on (with ) among stationary ergodic random conductances that permit jumps of arbitrary lengt…