Factor maps and embeddings for random \(\mathbb{Z}^d\) shifts of finite type (Q2631888)

The authors prove two results dealing with existence of factor maps and embeddings for random $\mathbb{Z}^d$-shift of finite type introduced by them in [J. Mod. Dyn. 10, 287--330 (2016; Zbl 1369.37023)]. Both results are based on a generalization of the second moment method allowing to obtain many patterns with prescribed repeated structure. \par Several open questions in this area are also presented at the end of article. One of them is related to the work of \textit{S. J. Lightwood} [Ergodic Theory Dyn. Syst. 23, No. 2, 587--609 (2003; Zbl 1031.37017)].