Characterization of sub‐Gaussian heat kernel estimates on strongly recurrent graphs

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Heat Kernels and Green Functions on Metric Measure Spaces (2014, background): “There are a vast literature to devote to some of these questions, for example, in [2, 6, 13, 14, 15, 17, 32, 33, 34, 36, 37, 38, 39] for the Euclidean spaces or Riemannian manifolds, in [8, 10, 24, 25] for torus or infinite graphs, in [3, 5, 9, 27] for certain classes of fractals and in [12, 26, 28,”
Heat Kernels on Metric Measure Spaces (2014, methodology): “In the strongly recurrent case α < β, it alone implies the elliptic Harnack inequality (H) so that two sided heat kernel estimates are equivalent to (Vα) + (Rβ) as was proved by Barlow, Coulhon, Kumagai [9] (in a setting of graphs) and was discussed in M.”
Off-diagonal upper estimates for the heat kernel of the Dirichlet forms on metric spaces (2008, unknown): “For strongly recurrent graphs, the reader may refer to [3].”