Heat Kernel Estimates Using Effective Resistance

  title={Heat Kernel Estimates Using Effective Resistance},
  author={Toshiya Kumagai},
In this chapter, we will study detailed asymptotic properties of Green functions and heat kernels using the effective resistance. Let (X, μ) be a weighted graph. We say that (X, μ) is a tree if for any l ≥ 3, there is no set of distinct points \(\{x_{i}\}_{i=1}^{l} \subset X\) such that x i ∼ x i+1 for 1 ≤ i ≤ l where we set \(x_{l+1}:= x_{1}\). 

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