Random Walks and Electrical Networks -- Max Ehrman

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Suppose you're given an electrical network, with each line segment
given some resistance and voltage. Then by relating conductance to
probability, we establish a correspondence between these electrical
networks and random walks. We will begin with a brief discussion of
Markov chains and Martingales, including some interesting examples
like the Ehrenfest diffusion model. We will also show the
probabilistic, Markov chain, and electrical network based proofs of
Rayleigh's Monotonicity Law. Finally we arrive at the main result:
Polya's Theorem, time permitting.
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