Quenched large deviation principle for words in a letter sequence (vol 148, pg 403, 2010)

In the article Quenched large deviation principle for words in a letter sequence, Probab. Theory Relat. Fields 148, no. 3/4 (2010), 403-456 we derived a quenched large deviation principle for the empirical process of words obtained by cutting an i.i.d. sequence of letters according to an independent renewal process. We derived a representation of the associated rate function for stationary word processes in terms of certain specific relative entropies. Our proof of this representation is correct when the mean word length is finite, but is flawed when the mean word length is infinite. In this paper we fix the flaw in the proof. Along the way we derive new representations of the rate function that are interesting in their own right. A key ingredient in the proof is the observation that if the rate function in the annealed large deviation principle is finite at a stationary word process, then the letters in the tail of the long words in this process are typical.