Continuous-time vertex reinforced jump processes on Galton-Watson trees
Abstract
We consider a continuous-time vertex reinforced jump process on a supercritical Galton-Watson tree. This process takes values in the set of vertices of the tree and jumps to a neighboring vertex with rate proportional to the local time at that vertex plus a constant . The walk is either transient or recurrent depending on this parameter . In this paper, we complete results previously obtained by Davis and Volkov [Probab. Theory Related Fields 123 (2002) 281-300, Probab. Theory Related Fields 128 (2004) 42-62] and Collevecchio [Ann. Probab. 34 (2006) 870-878, Electron. J. Probab. 14 (2009) 1936-1962] by proving that there is a unique (explicit) positive such that the walk is recurrent for and transient for .
Cite
@article{arxiv.1005.3607,
title = {Continuous-time vertex reinforced jump processes on Galton-Watson trees},
author = {Anne-Laure Basdevant and Arvind Singh},
journal= {arXiv preprint arXiv:1005.3607},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AAP811 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)