Abstract
We consider -dimensional directed polymers in a random potential and provide sufficient conditions guaranteeing joint localization. Joint localization means that for typical realizations of the environment, and for polymers started at different starting points, all the associated endpoint distributions localize in a common random region that does not grow with the length of the polymer. In particular, we prove that joint localization holds when the reference random walk of the polymer model is either a simple symmetric lattice walk or a Gaussian random walk. We also prove that the very strong disorder property holds for a large class of space-continuous polymer models, implying the usual single polymer localization.
Funding Statement
YB thanks NSF for partial support via grants DMS-1811444 and DMS-2243505.
Acknowledgments
We are grateful to Firas Rassoul-Agha for pointing out that our condition on the boundedness of partition functions can be easily derived from [27]. We are thankful to the referees for their detailed reading and useful comments.
Citation
Yuri Bakhtin. Douglas Dow. "Joint localization of directed polymers." Electron. J. Probab. 28 1 - 43, 2023. https://doi.org/10.1214/23-EJP1000
Information
