Abstract
In this chapter we collect some preliminary facts that we will need in the sequel. In Sect. 1.1 we introduce our basic notation related to subsets of \({\mathbb{Z}}^{d}\) and functions on \({\mathbb{Z}}^{d}\). In Sect. 1.2 we introduce simple random walk on \({\mathbb{Z}}^{d}\) and discuss properties of the Green function in the transient case d ≥ 3. In Sect. 1.3 we discuss the basics of potential theory, introduce the notion of equilibrium measure and capacity, and derive some of their properties.
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Drewitz, A., Ráth, B., Sapozhnikov, A. (2014). Random Walk, Green Function, and Equilibrium Measure. In: An Introduction to Random Interlacements. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-05852-8_1
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