Proof of the path localization conjecture for directed polymers
Probability
2019-09-04 v2 Mathematical Physics
math.MP
Abstract
It is a well-known open problem in the literature on random polymers to show that a directed polymer in random environment localizes around a favorite path at low temperature. A precise statement of this conjecture is formulated and proved in this article.
Keywords
Cite
@article{arxiv.1806.04220,
title = {Proof of the path localization conjecture for directed polymers},
author = {Sourav Chatterjee},
journal= {arXiv preprint arXiv:1806.04220},
year = {2019}
}
Comments
16 pages, 1 figure. To appear in Comm. Math. Phys