TY - JOUR
T1 - Random conductance models with stable-like jumps
T2 - Heat kernel estimates and Harnack inequalities
AU - Chen, Xin
AU - Kumagai, Takashi
AU - Wang, Jian
N1 - Funding Information:
The authors are very grateful to the referee for helpful suggestions and comments. The research of Xin Chen is supported by the National Natural Science Foundation of China (Nos. 11501361 and 11871338 ). The research of Takashi Kumagai is supported by JSPS KAKENHI Grant Number JP17H01093 and by the Alexander von Humboldt Foundation . The research of Jian Wang is supported by the National Natural Science Foundation of China (No. 11831014 ), the Program for Probability and Statistics: Theory and Application (No. IRTL1704 ) and the Program for Innovative Research Team in Science and Technology in Fujian Province University (IRTSTFJ).
Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/10/15
Y1 - 2020/10/15
N2 - We establish two-sided heat kernel estimates for random conductance models with non-uniformly elliptic (possibly degenerate) stable-like jumps on graphs. These are long range counterparts of the well known two-sided Gaussian heat kernel estimates by M.T. Barlow for nearest neighbor (short range) random walks on the supercritical percolation cluster. Unlike the cases of nearest neighbor conductance models, we cannot use parabolic Harnack inequalities since even elliptic Harnack inequalities do not hold in the present setting. As an application, we establish the local limit theorem for the models.
AB - We establish two-sided heat kernel estimates for random conductance models with non-uniformly elliptic (possibly degenerate) stable-like jumps on graphs. These are long range counterparts of the well known two-sided Gaussian heat kernel estimates by M.T. Barlow for nearest neighbor (short range) random walks on the supercritical percolation cluster. Unlike the cases of nearest neighbor conductance models, we cannot use parabolic Harnack inequalities since even elliptic Harnack inequalities do not hold in the present setting. As an application, we establish the local limit theorem for the models.
KW - Conductance models with stable-like jumps
KW - Dynkin-Hunt formula
KW - Harnack inequality
KW - Heat kernel estimate
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U2 - 10.1016/j.jfa.2020.108656
DO - 10.1016/j.jfa.2020.108656
M3 - Article
AN - SCOPUS:85085876377
SN - 0022-1236
VL - 279
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 7
M1 - 108656
ER -