On-diagonal lower estimate of heat kernels on graphs

Yong Lin Department of Mathematics, Renmin University of China, Beijing 100872, PR China Yiting Wu Department of Mathematics, Renmin University of China, Beijing 100872, PR China

Analysis of PDEs Combinatorics mathscidoc:2207.03003

Journal of Mathematical Analysis and Applications, 456, (2), 1040-1048, 2017.12
We establish a new on-diagonal lower estimate of continuous-time heat kernels for large time on graphs. To achieve the goal, we first introduce an upper estimate of heat kernels in natural graph metric, then use the upper estimate and the volume growth condition to show the validity of the on-diagonal lower estimate.
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@inproceedings{yong2017on-diagonal,
  title={On-diagonal lower estimate of heat kernels on graphs},
  author={Yong Lin, and Yiting Wu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707121852844220559},
  booktitle={Journal of Mathematical Analysis and Applications},
  volume={456},
  number={2},
  pages={1040-1048},
  year={2017},
}
Yong Lin, and Yiting Wu. On-diagonal lower estimate of heat kernels on graphs. 2017. Vol. 456. In Journal of Mathematical Analysis and Applications. pp.1040-1048. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220707121852844220559.
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