8 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, critical…
Quantitative stochastic homogenization for long-range random walks with critical jump index
Xin Chen, Chenlin Gu, Jian Wang
In this paper, we study the stochastic homogenization for a class of symmetric random walks in random conductance model, whose one-step transition probability from to is pr…
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 …
Quenched and annealed heat kernel estimates for Brox's diffusion
Xin Chen, Jian Wang
Brox's diffusion is a typical one-dimensional singular diffusion, which was introduced by Brox (1986) as a continuous analogue of Sinai's random walk. In this paper, we will establ…
Heat kernels and Green functions for fractional Schrödinger operators with confining potentials
Xin Chen, Kamil Kaleta, Jian Wang
We give two-sided, global (in all variables) estimates of the heat kernel and the Green function of the fractional Schrödinger operator with a non-negative and locally bounded pote…
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…
Sharp two-sided heat kernel estimates for Schrödinger operators with decaying potentials
Xin Chen, Jian Wang
We establish global two-sided heat kernel estimates (for full time and space) of the Schrödinger operator on , where the potential is locally bounded…