We continue the investigation of the localization phenomenon for a vertex reinforced random walk on the integer lattice. We provide some partial results towards a full characterization of the weights for which localization on 5 sites occurs with positive probability, and make some conjecture concerning the almost sure behavior.
"Localization on 5 sites for vertex reinforced random walks: Towards a characterization." Ann. Appl. Probab. 31 (4) 1774 - 1786, August 2021. https://doi.org/10.1214/20-AAP1633