Correction to: Quenched large deviation principle for words in a letter sequence (Probability Theory and Related Fields, (2010), 148, 3-4, (403-456), 10.1007/s00440-009-0235-5) - Birkner, Matthias; Greven, Andreas; Hollander, Frank den (Probability Theory and Related Fields, 2023)
Sections 1.1 and 1.2 (which are largely copied from [4, Sections 1.1- (Formula presented.) 1.2]) state the original theorem. Section 1.3 explains at what spot the original proof is flawed and how the flaw can be fixed. Section 1.4 provides further perspectives, lists the papers where the original theorem was used, and outlines the remainder of the paper. (Figure presented.) Cutting words from a letter sequence according to a renewal process Let E be a Polish space. View the elements of E as letters. Let (Formula presented.) be the set of finite words drawn from E, which is also a Polish space (see e.g. Remark A.9 in Appendix A; in case (Formula presented.) , we can simply use the discrete topology). Let (Formula presented.) and (Formula presented.) denote the set of probability measures on sequences drawn from E, respectively, (Formula presented.) , equipped with the topology of weak convergence. Write (Formula presented.) and (Formula presented.) for the left-shift acting on (Formula presented.) , respectively, (Formula presented.). Write (Formula presented.) and (Formula presented.) for the set of probability measures that are invariant, respectively, invariant and ergodic under (Formula presented.) , respectively, (Formula presented.). For (Formula presented.) , let (Formula presented.) be i.i.d. with marginal law (Formula presented.).
CRIS-Team Scopus Importer:2024-12-16
Keywords: Annealed vs. quenched; Empirical process; Large deviation principle; Letters and words; Rate function; Renewal process; Specific relative entropy