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ELECTRICAL NETWORKS AND REVERSIBLE MARKOV CHAINS

The object of this part of the course is to show how the mathematics of finite electrical networks can be used in the study of reversible Markov chains on finite and countable state spaces. The basis of the connection is that harmonic functions for reversible Markov chains can be interpreted as voltages for electrical networks. Thus, techniques for calculating, approximating, and bounding voltages (especially shorting and cutting) may be applied to problems involving harmonic functions (and, in particular, hitting probabilities).