@article{4e17ef81be22455983343f763209c73a,

title = "Strongly vertex-reinforced jump process on a complete graph",

abstract = "The aim of our work is to study vertex-reinforced jump processes with super-linear weight function w(t) = tα, for some α > 1. On any complete graph G = (V, E), we prove that there is one vertex v ∈ V such that the total time spent at v almost surely tends to infinity while the total time spent at the remaining vertices is bounded.",

keywords = "Non convergence to unstable equilibria, Nonlinear reinforcement, Random walks with memory, Stochastic approximation, Vertex-reinforced jump processes",

author = "Olivier Raimond and Nguyen, {Tuan Minh}",

note = "Funding Information: O. Raimond{\textquoteright}s research has been conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01) and of the project ANR MALIN (ANR-16-CE93-0003). T.M. Nguyen{\textquoteright}s research is partially supported by Crafoord Foundation and Thorild Dahlgren & Folke Lann{\'e}r Funds. The authors would like to thank the anonymous referees for their careful reading and their valuable suggestions which improved the manuscript. Publisher Copyright: {\textcopyright} Association des Publications de l{\textquoteright}Institut Henri Poincar{\'e}, 2021.",

year = "2021",

month = jul,

doi = "10.1214/20-AIHP1115",

language = "English",

volume = "57",

pages = "1549--1568",

journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",

issn = "0246-0203",

publisher = "Institute of Mathematical Statistics",

number = "3",

}