We introduce a system of strongly reinforced random walks on a cycle. Under certain conditions each particle localize on one edge. This result relies on the study of a generalized urn process which can be described as follows. The urn contains red and white balls. At each stage a ball is picked at random its color observed and returned to the urn with a ball of the same color. The probability to pick a ball of a given color is a function of the composition of the urn at that stage plus a "perturbation" which can be caused both by internal and external factors. Under a condition on the growth of the perturbation in time, we prove that the urn localizes on exactly one color.
This talk is based on joint works with J. Akahori, T. Garoni and K. Hamza.
Biography
Professor Collevecchio is a Senior Lecturer at Monash University, Australia. He received his PhD from the Purdue University, after which he has been a post-doc at the University of Chieti and at the Max Planck Institute in Lepzig, and Assistant Professor at the University of Venice. His research areas include interacting processes, large deviations, random graphs, and study of mixing times for markov chains.