Occupation measure for random walk on the circle (Q1900168)

Let \(0 = X_1, X_2, \ldots\) be a random walk on \(Z/pZ\) with transition probabilities \(\pi_{i,i - 1} = \pi_{i,i} = \pi_{i,i + 1} = 1/3\) with indices \(\text{mod} p\). The paper gives bounding probabilities of deviation of the relative occupation time of the process on an interval of the circle.