We will discuss a correlation theorem for pairs of locally Hölder continuous potentials with strong entropy gaps at infinity on a topologically mixing countable Markov shift with the BIP property. This extends a result of Lalley on shifts of finite type, and we will explain its application to the dynamics of (pairs of) Hitchin representations of a punctured surface. This talk is based on joint work in progress with Lien-Yung Nyima Kao.