Random Walks on ω-Networks

Abstract

A k-network, where k is any finite or transfinite, countable ordinal, is a transfinite generalization of an ordinary infinite electrical network. A prior work has established a theory for random walks on k-networks in the case where k is any natural number. The present work generalizes still further by establishing a theory for random walks on an ω-network, where ω is the first transfinite ordinal. It appears that such a theory can be established recursively for any ω-network by using the method of the prior work when proceeding to a successor ordinal and the method of the present work when proceeding to a limit ordinal.