Explicit estimates in the Bramson-Kalikow model
arXiv:1302.1267
Abstract
The aim of the present article is to explicitly compute parameters for which the Bramson-Kalikow model exhibits phase-transition. The main ingredient of the proof is a simple new criterion for non-uniqueness of -measures. We show that the existence of multiple -measures compatible with a function can be proved by estimating the -distances between some suitably chosen Markov chains. The method is optimal for the important class of binary regular attractive functions, which includes the Bramson-Kalikow model.
The title in the previous version has an error. We also changed the structure of the article so that the main result now is the explicit criterion for phase transition of the BK process. The new title reflects this change