4 papers
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…
Stochastic homogenization of diffusions in turbulence driven by non-local symmetric Lévy operators
Xin Chen, Jian Wang, Kun Yin
We investigate the stochastic homogenization of a class of turbulent diffusions generated by non-local symmetric Lévy operators with divergence-free drift fields in ergodic random…
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 pot…