abelian covering graphs over finite graphs). Actually it is possible to establish the central limit theorem and large deviation theorem in this setting.

As a Markov chain

A one-dimensional random walk can also be looked at as a Markov chain whose state space is given by the integers For some number p satisfying , the transition probabilities (the probability P_i,j of moving from state i to state j) are given by

Heterogeneous generalization

The heterogeneous random

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