Robert Makin
From CanisiusmathWiki
Over the summer I have a HMMI grant with Dr. Bisson to study Markov Chains. We are specifically interested about positive recurrence, null recurrence and transience on infinite Markov Chains. Some of the work is inspired by work done by Joshua O'Rourke at REU 2008, at this link Random Walks on Directed Multigraphs.
General example of positive recurrent infinite Markov Chain. Pick a node x in the graph.
For any (infinite) walk ω in the graph, let Nx(ω) count the
number of times that ω visits the node. The node x is said to be recurrent if
the expected value 
. This is a limit; we will explain all this later.
Doubly Stochastic Transition Matrices
Coverings and Markov Chains. We may start with Diane Lunman's examples at link An example of a family of left coverings
