I've been studying for quals for the last several weeks. Today, I was reviewing basic Markov Chain theory, and decided to understand it by drawing a graph of various statements about Markov Chains. Each statement is a node, and each edge is an implication, (so if A points to B then A implies B). If you're not familiar with the various definitions in the nodes, I'd recommend taking a look at Professor Lalley's very intuitive and readable lecture notes, or at Amir Dembo's comprehensive probability notes, which the edges in the graph below reference for proofs.
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