Abstract. We take a closer look at a class of chains with complete connections inspired by the one of Berger, Hoffman and Sidoravicius [1]. Besides giving a sharper description of the uniqueness and non-uniqueness regimes, we show that if the pure majority rule used to fix the dependence on the past is replaced with a function that is Lipschitz at the origin, then uniqueness always holds, even with arbitrarily slow decaying variation.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.