Perturbing subshifts of finite type: two words

TL;DR

This paper investigates how the entropy of irreducible subshifts of finite type changes when forbidden words are introduced, extending previous one-word results to two-word cases using correlation polynomials.

Contribution

It introduces multi-word correlation polynomials and analyzes their properties to bound entropy changes in the two-word perturbation scenario.

Findings

Established bounds on entropy change for two-word perturbations

Developed new methods involving correlation polynomials

Extended Lind's one-word bounds to the two-word case

Abstract

We bound the change in entropy incurred by an irreducible subshift of finite type upon perturbing it by forbidding a pair of admissible words. Lind has proven such bounds in the one-word case, and we adapt his methods. In particular, we introduce multi-word correlation polynomials and study their size, as well as that of their determinant in the two-word case.