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Coulhon, T. and Grigor’yan, A. (1997) On-Diagonal Lower Bounds for Heat Kernels on Non-Compact Manifolds and Markov Chains. Duke Mathematical Journal, 89, 133-199.

has been cited by the following article:

• TITLE: Heat Kernel Estimates on Simple Random Walks and On-Diagonal Upper Bounds

  AUTHORS: Runquan Zuo, Yuxiao Yan, Zishan Zhu, Liwen Yao, Qihao Han

  KEYWORDS: Heat Kernel, Simple Random Walk, On-Diagonal Estimate

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.10, October 31, 2024

  ABSTRACT: We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel.