## The Fundamental Matrix of a Finite Markov Chain

The purpose of this post is to present the very basics of potential theory for finite Markov chains. This post is by no means a complete presentation but rather aims to show that there are intuitive finite analogs of the potential kernels that arise when studying Markov chains on general state spaces. By presenting a piece of potential theory for Markov chains without the complications of measure theory I hope the reader will be able to appreciate the big picture of the general theory.